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