PROOF.ba.lb.ref: def of bend-osdev-algo@0.1.0.0 Import: import bend-osdev-algo@0.1.0.0/PROOF.bend as PROOF Lines 1437-1440 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=1437&end_line=1440 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 def ba.lb.ref(+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}, r: &l: List<&2, U32> -> {AR.Arrays.of_list(U32, d, l, 0) == a : Array} & {List.length(&2, U32, l) == AR.Arrays.slots(d) : Nat}) -> {U32.to_nat(Pair.snd(Array, U32, S.bsearch.array_lower_bound(a, n, key))) == S.bsearch.lower_bound(List.take(&2, U32, AR.Arrays.leaves(U32, a), U32.to_nat(n)), key) : Nat}: (l, e) = r (e1, hl) = e ba.lb.body(d, a, hd, n, hn, key, hs, l, e1, hl) Uses (21): https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Exists 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=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.to_nat https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=ba.lb.body https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/bsearch.bend&name=bsearch.array_lower_bound https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/bsearch.bend&name=bsearch.lower_bound 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-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.of_list https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.slots