proofs/containers/lru/read.bend checks
raw source on the hub · import bend-collections-laws-containers@1.0.0.0/proofs/containers/lru/read.bend as Read
36 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/math/u64.bend as W 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 ./bump.bend as BU import ./bumpsh.bend as BS import ./find.bend as FD import ./tfind.bend as TF import ./touch.bend as TO import ./touchsh.bend as TSH import ./rmat.bend as RM import ./gone.bend as GO 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 ../../lib/nat_list.bend as NL import ../../lib/words32.bend as W32 import ../../lib/u32_tree.bend as UT
Definitions
def lnz source · line 161 · raw
@+sd:Nat -> @+key:String -> @+b:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk -> @+hw:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.wb(sd, b) == True{} : Bool} -> @+hk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.hold(key, b) == True{} : Bool} -> {U32.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.lnk(b), 0) == False{} : Bool}
Templates
template rd_miss source · line 42 · raw
@-V:Data -> @+sh:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.Sh<V> -> @co:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/bumpsh.CountOK(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/bumpsh.cg_miss(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.model(V, sh)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fbump(&2, V, 4, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.real(V, sh))) -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/bumpsh.cg_miss(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.model(V, sh)), None{}), (0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fbump(&2, V, 4, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.real(V, sh)), None{}))a miss is counted
template rd_end0 source · line 49 · 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 -> @+now:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+tracked:Bool -> @+at:U32 -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.read_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, now, tracked, None{}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.rd_pick(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}), at, 0, now, tracked, True{}))
template rd_end 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> -> @+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 -> @+now:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+tracked:Bool -> @+at:U32 -> @+hf:{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) == None{} : Maybe<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Ent<V>>} -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.read_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, now, tracked, 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.rd_pick(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}), at, 0, now, tracked, True{}))
template l_on source · line 63 · raw
@-V:Data -> @l:0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V> -> U32
template l_life source · line 68 · raw
@-V:Data -> @l:0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V> -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64
template l_c source · line 73 · raw
@-V:Data -> @l:0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V> -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Ctr
template rd_tch source · line 78 · 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> -> @+key:String -> @+now:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+tracked:Bool -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+s:Nat -> @+hmem:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.memn(s, sl) == 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>} -> @+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} -> @+m2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+em:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.model(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, m2, k, sd, tabT, ksT, eT, lkT, sl, 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/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/spec/containers/lru.c_hit(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT)))} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V>} -> @-r:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.LRU<&2, V> -> @to:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/touchsh.TouchOK(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.L{cap, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, m2), 3n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.w64(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, m2), 4n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.snoc(V, 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), sl), key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/touch.ev(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), s, v)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, m2))}, r) -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.read_live(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/proofs/containers/lru/touch.ev(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), s, v), True{}), (r, Some{v}))
template rd_hitc source · line 88 · 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 -> @+now:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+tracked:Bool -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+s:Nat -> @+hmem:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.memn(s, sl) == 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>} -> @+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} -> @cm:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/bumpsh.CntM(V, cap, n, head, tail, free, mT, k, sd, tabT, ksT, eT, lkT, sl, 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/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/spec/containers/lru.c_hit(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT)))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fbump(&2, V, 3, 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/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.read_live(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/proofs/containers/lru/touch.ev(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), s, v), True{}), (0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.touch(&2, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fbump(&2, V, 3, 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})), su), Some{v}))
template rd_lv source · line 97 · 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 -> @+now:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+tracked:Bool -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+s:Nat -> @+hmem:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.memn(s, sl) == 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>} -> @+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/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.read_live(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/proofs/containers/lru/touch.ev(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), s, v), tracked), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.rd_live(&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}), su, tracked, v))a live entry read: tracked, it is counted and touched; untracked, nothing
template f_hsd 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> -> @+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} -> {Nat.is_lt(3n+sd, 32n) == True{} : Bool}
template f_s0 source · line 108 · 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} -> @+s:Nat -> @+hmem:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.memn(s, sl) == True{} : Bool} -> {Nat.is_lt(s, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(sd)) == True{} : Bool}
template rd_lf source · line 112 · 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 -> @+now:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+tracked:Bool -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+s:Nat -> @+hmem:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.memn(s, sl) == 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>} -> @+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/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.read_live(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/proofs/containers/lru/touch.ev(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), s, v), tracked), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.rd_live_f(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}), su, tracked))reading the value cell of a live slot
template rd_gn source · line 124 · raw
@-V:Data -> @+tracked:Bool -> @+sh2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.Sh<V> -> @+hg2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, sh2) == True{} : Bool} -> @+x:Maybe<&2, V> -> @+cap:U32 -> @+on:U32 -> @+life:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+es2:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Ent<V>> -> @+c:0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Ctr -> @+hm2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.L{cap, on, life, es2, c} == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.model(V, sh2) : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V>} -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.L{cap, on, life, es2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.c_miss_if(c, tracked)}, None{}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.rd_gone(&2, V, tracked, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.real(V, sh2), x)))after the removal of the expired entry: a miss, counted when tracked
template rd_ex2 source · line 131 · 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> -> @+key:String -> @+now:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+tracked:Bool -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+s:Nat -> @+hmem:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.memn(s, sl) == 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>} -> @+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} -> @-r:Pair(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.LRU<&2, V>, Maybe<&2, V>) -> @pk:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, (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), sl), key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.c_rm(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT)))}, Some{v}), r) -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, (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), sl), key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.c_miss_if(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.c_rm(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT))), tracked)}, None{}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.rd_gone(&2, V, tracked, r))
template rd_ex source · line 139 · 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 -> @+now:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+tracked:Bool -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+s:Nat -> @+hmem:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.memn(s, sl) == 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>} -> @+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} -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, (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), sl), key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.c_miss_if(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.c_rm(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT))), tracked)}, None{}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.rd_expire(&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}), su, U32.from_nat(i), tracked))an expired entry: removed, then read as a miss
template rd_gp source · line 146 · 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 -> @+now:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+tracked:Bool -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+s:Nat -> @+hmem:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.memn(s, sl) == 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>} -> @+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} -> @+g:Bool -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, Bool.pick(Pair(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V>, Maybe<&2, V>), g, (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), sl), key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.c_miss_if(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.c_rm(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT))), tracked)}, None{}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.read_live(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/proofs/containers/lru/touch.ev(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), s, v), tracked)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.rd_gone_pick(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}), su, U32.from_nat(i), tracked, g))
template rd_h source · line 154 · 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 -> @+now:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+tracked:Bool -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+s:Nat -> @+hmem:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.memn(s, sl) == 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>} -> @+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} -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.read_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, now, tracked, Some{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/touch.ev(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), s, v)}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.rd_hit(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}), su, U32.from_nat(i), now, tracked))a hit: the expiry test, then the live or the expired read
template rd_v0 source · line 169 · 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 -> @+now:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+tracked:Bool -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+s:Nat -> @+hmem:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.memn(s, sl) == True{} : Bool} -> @+su:U32 -> @+hsv:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(su) == 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.read_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, now, tracked, 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.rd_hit(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}), su, U32.from_nat(i), now, tracked))
template rd_hi source · line 180 · 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 -> @+now:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+tracked:Bool -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+i:Nat -> @+l:U32 -> @+hi:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hk0:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.hold(key, 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} -> @+hl:{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)) == l : U32} -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.read_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, now, tracked, 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.rd_pick(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}), U32.from_nat(i), l, now, tracked, U32.is_eq(l, 0)))
template rd_r source · line 191 · 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 -> @+now:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+tracked:Bool -> @+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.read_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, now, tracked, 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.rd_fd(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), now, tracked, 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))))
template rd_po 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> -> @+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 -> @+now:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+tracked:Bool -> @+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) -> @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.read_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, now, tracked, 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.rd_found(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), now, tracked, 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 read_sh source · line 221 · 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 -> @+now:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+tracked:Bool -> @+one:Nat -> @+h1:{one == 1n : Nat} -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.read(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, now, tracked), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.read(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, now, tracked))
template read_ok source · line 236 · 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 -> @+now:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64 -> @+tracked:Bool -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/rmat.POK(V, Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.read(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.model(V, sh), key, now, tracked), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.read(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.real(V, sh), key, now, tracked))THEOREM (read): get (tracked) and peek (untracked) are the specification's