proofs/containers/hash_table/insert.bend checks
raw source on the hub · import bend-collections-laws-containers@1.0.0.0/proofs/containers/hash_table/insert.bend as Insert
28 imports
import Base import ../../lib/logic.bend as L import ../../lib/nat.bend as N import ../../lib/u32.bend as U import ../../lib/array.bend as AR import ../../../spec/lib/common.bend as SC import ../../../spec/containers/hash_table.bend as S import ../../lib/word.bend as WD import ../../lib/u32div.bend as UD import ../../../src/math/hash.bend as HS import ../../../src/containers/hash_table.bend as H import ./words.bend as WR import ./strings.bend as STR import ./keys.bend as K import ./table.bend as TB import ./buckets.bend as B import ./modn.bend as M import ./cyc.bend as CY import ./arr.bend as AX import ./inv.bend as IV import ./state.bend as ST import ./probe_all.bend as PA import ./insm.bend as IM import ./insa.bend as IA import ./insu.bend as IU import ./insf.bend as IF import ../../lib/words32.bend as W32 import ../../lib/links.bend as LK
Definitions
def eq_is_eq source · line 36 · raw
@+a:Nat -> @+b:Nat -> @+h:{a == b : Nat} -> {Nat.is_eq(a, b) == True{} : Bool}
def kwnz_c source · line 39 · raw
@+c:U32 -> @+t:String -> @+sh:Bool -> {U32.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kw_c(c, t, sh), 0) == False{} : Bool}
def kword_nz source · line 47 · raw
@+key:String -> {U32.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0) == False{} : Bool}a key's word is never 0
def len_lt source · line 84 · raw
@-T:Data -> @+d:Nat -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<T> -> @+pf:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(T, d, t) == True{} : Bool} -> @+i:Nat -> @+h:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(d)) == True{} : Bool} -> {Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(T, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(T, t))) == True{} : Bool}
Templates
template s_sd source · line 56 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool}
template s32 source · line 59 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {Nat.is_lt(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/word.sc(32n, one)) == True{} : Bool}
template sl_eq source · line 63 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s) : Nat}slot(link(s)) = s
template ev source · line 66 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.from_nat(e)) == e : Nat}
template ix_h source · line 69 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {Nat.is_lt(1n+Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(1n+k)) == True{} : Bool}
template ix1 source · line 72 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))) == Nat.double(e) : Nat}
template ix2 source · line 75 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))) == 1n+Nat.double(e) : Nat}
template hi1 source · line 78 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(1n+k)) == True{} : Bool}
template hi2 source · line 81 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(1n+k)) == True{} : Bool}
template tab_eq source · line 89 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.put_bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, tabT), U32.from_nat(e), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s)) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s))) : Array<U32>}
template ks_eq source · line 95 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {Array.set(String, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(String, ksT), s, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key)) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(String, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))) : Array<String>}
template vs_eq source · line 98 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {Array.set(Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(Maybe<&2, V>, vsT), s, Some{x}) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, vsT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), Some{x})) : Array<Maybe<&2, V>>}
template real_eq source · line 102 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.ins_slot(&2, V, n, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k), td, fr, sz, sdU, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(Maybe<&2, V>, vsT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, nxT), s, U32.from_nat(e), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key), x, False{}) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.real(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.HS{U32.inc(n), k, td, fr, sz, sd, sdU, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, vsT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), Some{x}), nxT}) : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.HashMap<&2, V>}THEOREM: without growth, placing the entry builds the shadow's real map
template tab_slots source · line 112 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.update(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.update(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), Nat.double(e), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 1n+Nat.double(e), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s)) : List<&2, U32>}
template ks_slots source · line 120 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.update(String, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key)) : List<&2, String>}
template vs_slots source · line 123 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, vsT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), Some{x})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.update(Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s))), Some{x}) : List<&2, Maybe<&2, V>>}
template sl_sd source · line 126 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool}
template ns2 source · line 129 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool}
template bs2_eq source · line 133 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/insm.bupd(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s), key}) : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk>}THEOREM: the new shadow's buckets are the old ones with bucket e filled
template he_len source · line 141 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)))) == True{} : Bool}
template hs_len source · line 144 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT))) == True{} : Bool}
template sl_fr source · line 147 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool}
template g_well source · line 154 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.cwell(V, U32.inc(n), k, td, fr, sz, sd, sdU, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, vsT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), Some{x}), nxT) == True{} : Bool}
template g_clus source · line 158 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.cclus(V, U32.inc(n), k, td, fr, sz, sd, sdU, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, vsT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), Some{x}), nxT) == True{} : Bool}
template g_uniq source · line 161 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.cuniq(V, U32.inc(n), k, td, fr, sz, sd, sdU, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, vsT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), Some{x}), nxT) == True{} : Bool}
template g_n source · line 164 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.cn(V, U32.inc(n), k, td, fr, sz, sd, sdU, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, vsT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), Some{x}), nxT) == True{} : Bool}
template g_load source · line 171 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hov:{Nat.is_gt(Nat.double(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == False{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.cload(V, U32.inc(n), k, td, fr, sz, sd, sdU, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, vsT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), Some{x}), nxT) == True{} : Bool}
template g_live source · line 174 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.clive(V, U32.inc(n), k, td, fr, sz, sd, sdU, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, vsT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), Some{x}), nxT) == True{} : Bool}
template g_free source · line 179 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.cfree(V, U32.inc(n), k, td, fr, sz, sd, sdU, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, vsT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), Some{x}), nxT) == True{} : Bool}
template good2 source · line 190 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hov:{Nat.is_gt(Nat.double(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == False{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.goodF(V, U32.inc(n), k, td, fr, sz, sd, sdU, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, vsT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), Some{x}), nxT) == True{} : Bool}THEOREM: the placed entry keeps the invariant
template lk2 source · line 196 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+q:String -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/hash_table.lookup(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.model(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.HS{U32.inc(n), k, td, fr, sz, sd, sdU, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, vsT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), Some{x}), nxT}), q) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/hash_table.lookup(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/hash_table.set(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.absm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0n), key, x), q) : Maybe<&2, V>}
template sz2 source · line 201 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/hash_table.size(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.model(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.HS{U32.inc(n), k, td, fr, sz, sd, sdU, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(s)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(String, sd, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, vsT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), Some{x}), nxT})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/hash_table.size(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/hash_table.set(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.absm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0n), key, x)) : Nat}
template SetM source · line 208 · raw
@-V:Data -> @+m:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/hash_table.Entry<V>> -> @+key:String -> @+x:V -> @r:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.HashMap<&2, V> -> Type
the result of an update: a good shadow whose model agrees with the specification's set on every lookup and on the size
template ins_nogrow source · line 213 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fr:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+s:U32 -> @+e:Nat -> @+key:String -> @+x:V -> @+hk31:{Nat.is_lt(k, 31n) == True{} : Bool} -> @+hk0:{Nat.is_lt(0n, k) == True{} : Bool} -> @+hsd:{Nat.is_lt(sd, 32n) == True{} : Bool} -> @+hsdk:{Nat.is_lt(sd, k) == True{} : Bool} -> @+pt:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT) == True{} : Bool} -> @+pk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(String, sd, ksT) == True{} : Bool} -> @+pv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(Maybe<&2, V>, sd, vsT) == True{} : Bool} -> @+pn:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, sd, nxT) == True{} : Bool} -> @+htd:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(td), 1n+k) == True{} : Bool} -> @+hsz:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool} -> @+hsdu:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sdU), sd) == True{} : Bool} -> @+hwell:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PWell{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)) == True{} : Bool} -> @+huq:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PUniq{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hcn:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool} -> @+hld:{Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.lvs(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hfr:{Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(sz)) == True{} : Bool} -> @+hnf:{Nat.is_le(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hfl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.fl_ok(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, nxT), Nat.sub(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr), [0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s)]) == True{} : Bool} -> @+hs:{Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(fr)) == True{} : Bool} -> @+hns:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.noslot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), e)) == True{} : Bool} -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hovi:{U32.is_gt(U32.shl(U32.inc(n)), U32.inc(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))) == False{} : Bool} -> SetM(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.absm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, vsT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0n), key, x, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.ins_slot(&2, V, n, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k), td, fr, sz, sdU, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(Maybe<&2, V>, vsT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, nxT), s, U32.from_nat(e), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key), x, U32.is_gt(U32.shl(U32.inc(n)), U32.inc(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k)))))THEOREM: placing a new entry without growing the table refines set