PROOF.ba.fl.body: def of bend-osdev-algo@0.1.0.0 Import: import bend-osdev-algo@0.1.0.0/PROOF.bend as PROOF Lines 1453-1460 of bend-osdev-algo@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&start_line=1453&end_line=1460 import Base import bend-osdev-algo@0.1.0.0/bsearch.bend as S import bend-osdev-array@0.1.0.0/array.bend as AR import bend-osdev-array@0.1.0.0/LAWS.bend as AL import bend-osdev-algo@0.1.0.0/proof_bsearch.bend as Q import bend-osdev-algo@0.1.0.0/LAWS.bend as Laws def ba.fl.body(+d: Nat, -a: Array, +hd: {Nat.is_lt(d, 32n) == True{} : Bool}, +n: U32, +hn: {Nat.is_le(U32.to_nat(n), AR.Arrays.slots(d)) == True{} : Bool}, +key: U32, hs: {S.bsearch.sorted(List.take(&2, U32, AR.Arrays.leaves(U32, a), U32.to_nat(n))) == True{} : Bool}, +l: List<&2, U32>, +e1: {AR.Arrays.of_list(U32, d, l, 0) == a : Array}, +hl: {List.length(&2, U32, l) == AR.Arrays.slots(d) : Nat}) -> {Laws.algo_index_nat(Pair.snd(Array, Maybe<&2, U32>, S.bsearch.array_find(a, n, key))) == S.bsearch.find(List.take(&2, U32, AR.Arrays.leaves(U32, a), U32.to_nat(n)), key) : Maybe<&2, Nat>}: -ol = AR.Arrays.of_list(U32, d, l, 0) +r = Q.bq.run(33n, d, l, 0, n, key) %e1 : {Laws.algo_index_nat(Pair.snd(Array, Maybe<&2, U32>, S.bsearch.array_find(_, n, key))) == S.bsearch.find(List.take(&2, U32, AR.Arrays.leaves(U32, _), U32.to_nat(n)), key) : Maybe<&2, Nat>} %Equal.sym(List<&2, U32>, AR.Arrays.leaves(U32, ol), l, AL.of_list_leaves(U32, d, l, 0, hl)) : {Laws.algo_index_nat(Pair.snd(Array, Maybe<&2, U32>, S.bsearch.array_find(ol, n, key))) == S.bsearch.find(List.take(&2, U32, _, U32.to_nat(n)), key) : Maybe<&2, Nat>} %Equal.sym(Array & U32, S.bsearch.array.go(33n, S.BsearchState{ol, 0, n}, key), (ol, r), Q.bq.go(33n, d, l, hl, hd, 0, n, key)) : {Laws.algo_index_nat(Pair.snd(Array, Maybe<&2, U32>, S.bsearch.array.find(_, n, key))) == S.bsearch.find(Q.bq.pre(l, n), key) : Maybe<&2, Nat>} %Equal.sym(Array & U32, Array.get(U32, ol, r), (ol, AR.Arrays.nth(U32, l, AR.Arrays.index(d, r), 0)), AL.of_list_get(U32, d, l, 0, hl, hd, r)) : {Laws.algo_index_nat(Pair.snd(Array, Maybe<&2, U32>, S.bsearch.array.found(U32.is_lt(r, n), _, r, key))) == S.bsearch.find(Q.bq.pre(l, n), key) : Maybe<&2, Nat>} ba.fd(U32.is_lt(r, n), d, l, hl, key, n, hn, r, {==}, ba.answer(d, l, hl, key, n, hn, ba.hs(d, a, l, n, e1, hl, hs))) Uses (38): https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array.get https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.take https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair.snd https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32 https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_lt https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/LAWS.bend&name=algo_index_nat https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=ba.answer https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=ba.fd https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=ba.hs https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/bsearch.bend&name=BsearchState https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/bsearch.bend&name=bsearch.array.find https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/bsearch.bend&name=bsearch.array.found https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/bsearch.bend&name=bsearch.array.go https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/bsearch.bend&name=bsearch.array_find https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/bsearch.bend&name=bsearch.find https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/bsearch.bend&name=bsearch.sorted https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/proof_bsearch.bend&name=bq.go https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/proof_bsearch.bend&name=bq.pre https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/proof_bsearch.bend&name=bq.run https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/LAWS.bend&name=of_list_get https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/LAWS.bend&name=of_list_leaves https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.index https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.leaves https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.nth https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.of_list https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.slots