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proofs/containers/lru/grow.bend checks

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

38 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/keys.bend as K
import ./state.bend as ST
import ./basic.bend as BA
import ./bumpsh.bend as BS
import ./unlink.bend as UL
import ./meta.bend as MT
import ../../../src/math/hash.bend as HS
import ../hash_table/probe_all.bend as PA
import ./read.bend as RD
import ./ins.bend as IC
import ./insp.bend as IP
import ./pre.bend as PR
import ./room.bend as RO
import ../hash_table/arena.bend as AN
import ../hash_table/insgrow.bend as IG
import ./ins1.bend as I1
import ../../lib/u32.bend as U
import ../hash_table/insert.bend as IS
import ../hash_table/modn.bend as M
import ../../lib/links.bend as LK
import ../../lib/words32.bend as W32
import ../../lib/u32_tree.bend as UT

Templates

template gw_good source · line 48 · 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> -> @+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, []}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+hroom:{Nat.is_le(Nat.double(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hr:{U32.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 0n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 1n)) == False{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.good(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.LS{cap, n, head, tail, free, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 5n, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 5n, mT, 1n, U32.shl(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 1n))), 2n, U32.inc(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 2n))), k, 1n+sd, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.TNode{ksT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.trep(String, sd, "")}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.TNode{eT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.trep(Maybe<&2, V>, sd, None{})}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.TNode{lkT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.trep(U32, 3n+sd, 0)}, sl, []}) == True{} : Bool}

THEOREM: the doubled arena keeps the invariant

template gw_es source · line 77 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+sl: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, []}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+hroom:{Nat.is_le(Nat.double(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hr:{U32.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 0n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 1n)) == False{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.es(V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, lkT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.trep(U32, 3n+sd, 0))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(String, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.trep(String, sd, ""))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, eT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(Maybe<&2, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.trep(Maybe<&2, V>, sd, None{}))), sl) == 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) : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.Ent<V>>}

... and the model's entries

template igr_n source · line 98 · raw

@-V:Data -> @+cap:U32 -> @+n:U32 -> @+head:U32 -> @+tail:U32 -> @+free:U32 -> @+mT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+k:Nat -> @+sd:Nat -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @+eT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+lkT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+sl: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, []}) == True{} : Bool} -> @+one:Nat -> @+h1:{one == 1n : Nat} -> @+key:String -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+e:Nat -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{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)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/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))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(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))), e)) == True{} : Bool} -> @+hroom:{Nat.is_le(Nat.double(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+v:V -> @+t:U32 -> @+lo:U32 -> @+hi:U32 -> @+free2:U32 -> @+hf2:{U32.is_eq(free2, 0) == True{} : Bool} -> @+hr:{U32.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 0n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 1n)) == False{} : Bool} -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/bumpsh.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/spec/containers/lru.snoc(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), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.LE{key, v, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64{lo, hi}}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.c_ins(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT)))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fresh_room(&2, V, cap, n, head, tail, free2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 0n)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(Maybe<&2, V>, eT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, lkT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.E{v, t, lo, hi}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 0n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 1n), False{}))

template ip_grow source · line 164 · 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} -> @+key:String -> @+hno:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.all_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.PNo{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/table.buckets(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, tabT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)), key}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+e:Nat -> @+he:{Nat.is_lt(e, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+hz:{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)), e) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.BE{} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.occpath(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/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))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/modn.dist(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))), e)) == True{} : Bool} -> @+hroom:{Nat.is_le(Nat.double(1n+0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(n)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.pow2(k)) == True{} : Bool} -> @+v:V -> @+t:U32 -> @+lo:U32 -> @+hi:U32 -> @+free2:U32 -> @+hf2:{U32.is_eq(free2, 0) == True{} : Bool} -> @+hfz:{U32.is_eq(free, 0) == True{} : Bool} -> @+hr:{U32.is_lt(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 0n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 1n)) == False{} : Bool} -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/bumpsh.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/spec/containers/lru.snoc(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), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.LE{key, v, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/math/u64.U64{lo, hi}}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/lru.c_ins(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/lru/state.ctr(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT)))}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.fresh_room(&2, V, cap, n, head, tail, free2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, mT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.upd(U32, 1n+k, tabT, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.shl(U32.from_nat(e))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/u32div.v(U32.inc(U32.shl(U32.from_nat(e)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.link(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 0n)))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(String, ksT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(Maybe<&2, V>, eT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.thaw(U32, lkT), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/probe_all.stored(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/keys.kword(key), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/lru.E{v, t, lo, hi}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 0n), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/words32.nth0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.slots(U32, mT), 1n), False{}))

THEOREM (add, a full arena: it doubles and the fresh slot takes the entry)