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proofs/containers/lru/bumpsh.bend checks

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

11 imports
import Base
import ../../lib/nat.bend as N
import ../../lib/array.bend as AR
import ../../../spec/lib/common.bend as SC
import ../../../spec/containers/lru.bend as SP
import ../../../src/containers/lru.bend as LR
import ./state.bend as ST
import ./meta.bend as MT
import ./basic.bend as BA
import ./bump.bend as BU
import ../../lib/words32.bend as W32

Definitions

def lo8 source · line 19 · raw

@+i:Nat -> @+h8:{Nat.is_le(8n, i) == True{} : Bool} -> @+j:Nat -> @+hj:{Nat.is_lt(j, 8n) == True{} : Bool} -> {Nat.is_eq(i, j) == False{} : Bool}

def lo8s source · line 22 · raw

@+i:Nat -> @+h8:{Nat.is_le(8n, i) == True{} : Bool} -> @+j:Nat -> @+hj:{Nat.is_lt(j, 8n) == True{} : Bool} -> {Nat.is_eq(1n+i, j) == False{} : Bool}

def keep source · line 25 · raw

@+ml:List<&2, U32> -> @+m2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+i:Nat -> @+x:U32 -> @+y:U32 -> @+e:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, m2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.update(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.update(U32, ml, i, x), 1n+i, y) : List<&2, U32>} -> @+j:Nat -> @+h1:{Nat.is_eq(i, j) == False{} : Bool} -> @+h2:{Nat.is_eq(1n+i, j) == False{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, m2), j) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(ml, j) : U32}

Templates

template CountOK source · line 16 · raw

@-V:Data -> @+spec:0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V> -> @r:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.LRU<&2, V> -> Type

template bm_fin source · line 30 · 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} -> @+i:Nat -> @+h8:{Nat.is_le(8n, i) == True{} : Bool} -> @+m2:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+pm2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.perfect(U32, 5n, m2) == True{} : Bool} -> @+x:U32 -> @+y:U32 -> @+e:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, m2) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.update(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.update(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), i, x), 1n+i, y) : List<&2, U32>} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, m2, k, sd, tabT, ksT, eT, lkT, sl, fl}) == True{} : Bool}

the meta words of m2: i and i + 1 written, the invariant's words kept

template count_ins source · line 34 · 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} -> @bo:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/bump.BumpOK(mT, 16n, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.bump(0, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT))) -> CountOK(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/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_ins(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT)))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fbump(&2, V, 0, 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})))

template count_ev source · line 46 · 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} -> @bo:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/bump.BumpOK(mT, 18n, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.bump(1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT))) -> CountOK(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/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_ev(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT)))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fbump(&2, V, 1, 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})))

template count_rm source · line 58 · 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} -> @bo:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/bump.BumpOK(mT, 20n, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.bump(2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT))) -> CountOK(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/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_rm(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT)))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fbump(&2, V, 2, 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})))

template count_hit source · line 70 · 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} -> @bo:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/bump.BumpOK(mT, 22n, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.bump(3, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT))) -> CountOK(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/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})))

template count_miss source · line 82 · 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} -> @bo:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/bump.BumpOK(mT, 24n, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.bump(4, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT))) -> CountOK(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/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_miss(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT)))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fbump(&2, V, 4, 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})))

template CntM source · line 96 · 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> -> @+spec:0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V> -> @r:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.LRU<&2, V> -> Type

template cntm_ins source · line 99 · 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} -> @bo:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/bump.BumpOK(mT, 16n, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.bump(0, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT))) -> 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_ins(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT)))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fbump(&2, V, 0, 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})))

template cg_ins source · line 110 · raw

@-V:Data -> @l:0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V> -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V>

template countg_ins source · line 116 · raw

@-V:Data -> @+sh:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.Sh<V> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, sh) == True{} : Bool} -> CountOK(V, cg_ins(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.model(V, sh)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fbump(&2, V, 0, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.real(V, sh)))

THEOREM: fbump(0) counts on any shadow

template cntm_ev 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> -> @+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} -> @bo:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/bump.BumpOK(mT, 18n, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.bump(1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT))) -> 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_ev(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT)))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fbump(&2, V, 1, 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})))

template cg_ev source · line 132 · raw

@-V:Data -> @l:0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V> -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V>

template countg_ev source · line 138 · raw

@-V:Data -> @+sh:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.Sh<V> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, sh) == True{} : Bool} -> CountOK(V, cg_ev(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.model(V, sh)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fbump(&2, V, 1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.real(V, sh)))

THEOREM: fbump(1) counts on any shadow

template cntm_rm 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> -> @+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} -> @bo:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/bump.BumpOK(mT, 20n, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.bump(2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT))) -> 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_rm(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT)))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fbump(&2, V, 2, 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})))

template cg_rm source · line 154 · raw

@-V:Data -> @l:0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V> -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V>

template countg_rm source · line 160 · raw

@-V:Data -> @+sh:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.Sh<V> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, sh) == True{} : Bool} -> CountOK(V, cg_rm(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.model(V, sh)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fbump(&2, V, 2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.real(V, sh)))

THEOREM: fbump(2) counts on any shadow

template cntm_hit 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> -> @+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} -> @bo:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/bump.BumpOK(mT, 22n, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.bump(3, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT))) -> 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})))

template cg_hit source · line 176 · raw

@-V:Data -> @l:0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V> -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V>

template countg_hit source · line 182 · raw

@-V:Data -> @+sh:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.Sh<V> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, sh) == True{} : Bool} -> CountOK(V, cg_hit(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.model(V, sh)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fbump(&2, V, 3, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.real(V, sh)))

THEOREM: fbump(3) counts on any shadow

template cntm_miss source · line 187 · 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} -> @bo:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/bump.BumpOK(mT, 24n, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.bump(4, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT))) -> 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_miss(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT)))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fbump(&2, V, 4, 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})))

template cg_miss source · line 198 · raw

@-V:Data -> @l:0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V> -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Lru<V>

template countg_miss source · line 204 · raw

@-V:Data -> @+sh:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.Sh<V> -> @+hg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, sh) == True{} : Bool} -> CountOK(V, 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)))

THEOREM: fbump(4) counts on any shadow