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proofs/containers/lru/rmrb.bend checks

raw source on the hub · import bend-collections-laws-containers@1.0.0.0/proofs/containers/lru/rmrb.bend as Rmrb

41 imports
import Base
import ../../lib/logic.bend as L
import ../../lib/nat.bend as N
import ../../lib/u32.bend as U
import ../../lib/u32alg.bend as A
import ../../lib/array.bend as AR
import ../../lib/list.bend as LL
import ../../../spec/lib/common.bend as SC
import ../../../spec/containers/hash_table.bend as S
import ../../../spec/containers/lru.bend as SP
import ../../lib/u32div.bend as UD
import ../../../src/containers/hash_table.bend as H
import ../../../src/containers/lru.bend as LR
import ../hash_table/table.bend as TB
import ../hash_table/buckets.bend as B
import ../hash_table/cyc.bend as CY
import ../hash_table/inv.bend as IV
import ../hash_table/state.bend as HT
import ../hash_table/insm.bend as IM
import ../hash_table/insa.bend as IA
import ../hash_table/tools.bend as TL
import ../hash_table/poplem.bend as PL
import ../hash_table/delmv.bend as DM
import ../hash_table/delw.bend as DW
import ./state.bend as ST
import ./lists.bend as LS
import ./dll.bend as DL
import ./trace.bend as TR
import ./unlink.bend as UL
import ./linktail.bend as LT
import ./rebuild.bend as RB
import ./perm.bend as PE
import ./tabsl.bend as TS
import ./elfr.bend as EF
import ../hash_table/insf.bend as IF
import ./idx.bend as ID
import ./touchsh.bend as TSH
import ../../lib/nat_list.bend as NL
import ../../lib/links.bend as LK
import ../../lib/words32.bend as W32
import ../../lib/u32_tree.bend as UT

Templates

template f_sd source · line 50 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {Nat.is_lt(3n+sd, 32n) == True{} : Bool}

template f_mid source · line 53 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {Bool.and(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b)), Bool.not(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.memn(s, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b)))) == True{} : Bool}

template f_ndY source · line 56 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b)) == True{} : Bool}

template f_sn source · line 59 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.memn(s, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b)) == False{} : Bool}

template f_sX source · line 62 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.memn(s, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool}

template f_sub source · line 65 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/insf.subl(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool}

template f_bY source · line 68 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.sall(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.PLive{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 0n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b)) == True{} : Bool}

template f_ls source · line 71 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {Bool.and(Nat.is_lt(s, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 0n))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.live(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s)) == True{} : Bool}

template f_s0 source · line 74 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {Nat.is_lt(s, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool}

template f_sf source · line 77 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.memn(s, fl) == False{} : Bool}

template f_su source · line 80 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {Nat.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool}

template f_sd32 source · line 83 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {Nat.is_lt(sd, 32n) == True{} : Bool}

template f_eu source · line 87 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, eT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su), None{})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.update(Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s, None{}) : List<&2, Maybe<&2, V>>}

the vacated value cells

template f_lu source · line 91 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 3n+sd, t2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.nidx(su)), free)) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.TW{s, 1n, free, tr}) : List<&2, U32>}

the free-list push

template f_tlo source · line 95 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.TW{s, 1n, free, tr}) == True{} : Bool}

template f_len source · line 98 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b)) : Nat}

template f_n source · line 102 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n) == 1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b)) : Nat}

the count, one lower

template f_n1 source · line 105 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.sub(n, 1)) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b)) : Nat}

template d1 source · line 113 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 1n+k, tabT2) == True{} : Bool}

template d2 source · line 115 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.cluster(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT2), 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}

template d3 source · line 117 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {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, tabT2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool}

template d4 source · line 119 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PFrom{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool}

template d5 source · line 121 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PTo{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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool}

template d6 source · line 123 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool}

template f_blen source · line 126 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {Nat.is_lt(i, 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 c_well source · line 129 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {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, tabT2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), sd}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool}

template c_n source · line 132 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.sub(n, 1)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/inv.occn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k))) == True{} : Bool}

template f_n1le source · line 140 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {Nat.is_le(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.sub(n, 1)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)) == True{} : Bool}

template c_load source · line 143 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {Nat.is_le(Nat.double(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.sub(n, 1))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool}

template c_bsl source · line 149 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.bsl(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 3n+sd, t2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.nidx(su)), free)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool}

template c_has source · line 155 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.hasall(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT2), 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, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 3n+sd, t2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.nidx(su)), free)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b)) == True{} : Bool}

template c_sl source · line 165 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.slok(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 0n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, eT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su), None{}))) == True{} : Bool}

template c_len source · line 168 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.sub(n, 1))) == True{} : Bool}

template c_dll source · line 171 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 3n+sd, t2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.nidx(su)), free)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool}

template f_es source · line 177 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.es(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 3n+sd, t2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.nidx(su)), free)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, eT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su), None{})), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b)) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.es(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b)) : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Ent<V>>}

the new model's entries are the old ones of a ++ b

template c_keys source · line 184 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/hash_table.nodup(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.keys_of(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.es(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 3n+sd, t2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.nidx(su)), free)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, eT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su), None{})), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b)))) == True{} : Bool}

template c_free source · line 197 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {U32.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(su), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/links.fst_or(s <> fl, 0)) == True{} : Bool}

template c_fll source · line 200 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.fll(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 3n+sd, t2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.nidx(su)), free)), s <> fl) == True{} : Bool}

template c_fl source · line 208 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.flok(V, s <> fl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 0n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, eT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su), None{}))) == True{} : Bool}

template c_fnd source · line 215 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(s <> fl) == True{} : Bool}

template c_fcnt source · line 218 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {Nat.is_eq(Nat.add(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(Nat, s <> fl)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 0n))) == True{} : Bool}

template good_rm source · line 225 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, U32.sub(n, 1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/links.fst_or(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/links.last_or(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(su), mT, k, sd, tabT2, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, eT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su), None{}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 3n+sd, t2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.nidx(su)), free), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), s <> fl}) == True{} : Bool}

THEOREM: the invariant after the removal

template model_rm source · line 231 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+a:List<&2, Nat> -> @+s:Nat -> @+b:List<&2, Nat> -> @+fl:List<&2, Nat> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b), fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hoi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occ(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)), i)) == True{} : Bool} -> @+hsi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(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)), i)))) == s : Nat} -> @+tabT2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+hd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/delw.dfin2(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 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)), i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{}), tabT2) == True{} : Bool} -> @+t2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+tr:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.Tr -> @+hp2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 3n+sd, t2) == True{} : Bool} -> @+hs2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.app(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), tr) : List<&2, U32>} -> @+hlo:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trlo(tr) == True{} : Bool} -> @+hin:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/trace.trin(tr, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)) == True{} : Bool} -> @+hseg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.seg(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, t2), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0, 0) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == s : Nat} -> @+v:V -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == Some{v} : Maybe<&2, V>} -> @+key:String -> @+hk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/hash_table.str_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.skey(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), s), key) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.model(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, U32.sub(n, 1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/links.fst_or(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/links.last_or(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), 0), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(su), mT, k, sd, tabT2, ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(Maybe<&2, V>, sd, eT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su), None{}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 3n+sd, t2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.nidx(su)), free), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, b), s <> fl}) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.L{cap, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 3n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.w64(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 4n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.drop(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.es(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, a, s <> b)), key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT))} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V>}

THEOREM: the model after the removal is the specification's drop of key