proofs/containers/lru/remove.bend checks
raw source on the hub · import bend-collections-laws-containers@1.0.0.0/proofs/containers/lru/remove.bend as Remove
33 imports
import Base import ../../lib/logic.bend as L import ../../lib/nat.bend as N import ../../lib/u32alg.bend as A import ../../lib/array.bend as AR 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/keys.bend as K import ./state.bend as ST import ./basic.bend as BA import ./find.bend as FD import ./tfind.bend as TF import ./touch.bend as TO import ./rmat.bend as RM import ./unlink.bend as UL import ../hash_table/get.bend as G import ../../../src/math/hash.bend as HS import ../hash_table/probe_impl.bend as PI import ../hash_table/probe_all.bend as PA import ./read.bend as RD import ./qrm.bend as QR import ../../lib/nat_list.bend as NL import ../../lib/words32.bend as W32 import ../../lib/u32_tree.bend as UT
Templates
template rm_v0 source · line 40 · 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> -> @+sl: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, sl, fl}) == True{} : Bool} -> @+key:String -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+s:Nat -> @+hmem:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.memn(s, sl) == True{} : Bool} -> @+l:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(l)) == s : Nat} -> @+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} -> @+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} -> @+m:Maybe<&2, V> -> @+hmm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.nthm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), s) == m : Maybe<&2, V>} -> @+hsm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/state.some_b(V, m) == True{} : Bool} -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.remove_found(V, 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/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), sl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT)), key, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.find(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), sl), key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.drop_slot(&2, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.F{cap, n, head, tail, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.del_at(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k), U32.from_nat(i)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(Maybe<&2, V>, eT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, lkT)}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.slot(l), 2))
template rm_res source · line 51 · 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> -> @+sl: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, sl, fl}) == True{} : Bool} -> @+key:String -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+h:Nat -> @+r0:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Res -> @hres:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.ResOK(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), h, key, r0) -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.remove_found(V, 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/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), sl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT)), key, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.find(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), sl), key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/qrm.qrm_of(V, r0, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k), cap, n, head, tail, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(Maybe<&2, V>, eT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, lkT)))the probe's result, then the removal it asks for
template lp_fd source · line 73 · 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> -> @+sl: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, sl, fl}) == True{} : Bool} -> @+key:String -> @+h:Nat -> @+r0:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Res -> @hres:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.ResOK(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), h, key, r0) -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.rm_fd(&2, V, cap, n, head, tail, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(Maybe<&2, V>, eT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, lkT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_impl.fd_of(r0, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/qrm.qrm_of(V, r0, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k), cap, n, head, tail, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(Maybe<&2, V>, eT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, lkT)) : Pair(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.LRU<&2, V>, Maybe<&2, V>)}the long path's result read back as the removal the probe asks for
template rm_po 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> -> @+sl: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, sl, fl}) == True{} : Bool} -> @+key:String -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+r0:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Res -> @hres:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.ResOK(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), key, r0) -> @hresb:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.ResOK(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/hash.bucket(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k))), key, r0) -> @po:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.ProbeOK(tabT, sd, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), r0, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.probe(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k), key)) -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.remove_found(V, 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/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), sl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT)), key, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.find(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), sl), key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.rm_found(&2, V, cap, n, head, tail, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(Maybe<&2, V>, eT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, lkT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.probe(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/cyc.msk(k), key)))
template rm_long source · line 103 · 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> -> @+sl: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, sl, fl}) == True{} : Bool} -> @+key:String -> @+one:Nat -> @+h1:{one == 1n : Nat} -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.remove(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.model(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, sl, fl}), key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.remove_long(&2, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.real(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, sl, fl}), key))the long path: probe, then remove at the found bucket
template rm_short source · line 110 · 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> -> @+sl: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, sl, fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+c:U32 -> @+hc:{U32.is_lt(c, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.tag) == True{} : Bool} -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.remove(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.model(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, sl, fl}), {SCon{Chr{c}, ""} : String}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.rm_q(&2, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.real(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, sl, fl}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.short_word(c)))the fused one-character path
template rm_sh source · line 120 · 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> -> @+sl: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, sl, fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+c:U32 -> @+b:Bool -> @+hb:{U32.is_lt(c, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.tag) == b : Bool} -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.remove(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.model(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, sl, fl}), {SCon{Chr{c}, ""} : String}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.rm_short(&2, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.real(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, sl, fl}), c, b))
template rm_ch source · line 127 · 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> -> @+sl: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, sl, fl}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+c:U32 -> @+t:String -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.remove(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.model(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, sl, fl}), SCon{Chr{c}, t}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.rm_c(&2, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.real(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, sl, fl}), c, t))
template remove_sh source · line 134 · 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> -> @+sl: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, sl, fl}) == True{} : Bool} -> @+key:String -> @+one:Nat -> @+h1:{one == 1n : Nat} -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.remove(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.model(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, sl, fl}), key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.remove(&2, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.real(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, sl, fl}), key))
template remove_ok source · line 142 · raw
@-V:Data -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+sh:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.Sh<V> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, sh) == True{} : Bool} -> @+key:String -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.remove(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.model(V, sh), key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.remove(&2, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.real(V, sh), key))THEOREM (remove): the specification's remove