PROOF.ba.fls.body: def of bend-osdev-algo@0.1.0.0
Import: import bend-osdev-algo@0.1.0.0/PROOF.bend as PROOF
Lines 1467-1473 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=1467&end_line=1473

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

def ba.fls.body(+d: Nat, -a: Array<U32>, +hd: {Nat.is_lt(d, 32n) == True{} : Bool}, +n: U32, +key: U32, +l: List<&2, U32>, +e1: {AR.Arrays.of_list(U32, d, l, 0) == a : Array<U32>}, +hl: {List.length(&2, U32, l) == AR.Arrays.slots(d) : Nat}) -> {Pair.fst(Array<U32>, Maybe<&2, U32>, S.bsearch.array_find(a, n, key)) == a : Array<U32>}:
  -ol = AR.Arrays.of_list(U32, d, l, 0)
  +r = Q.bq.run(33n, d, l, 0, n, key)
  %e1 : {Pair.fst(Array<U32>, Maybe<&2, U32>, S.bsearch.array_find(_, n, key)) == _ : Array<U32>}
  %Equal.sym(Array<U32> & 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)) : {Pair.fst(Array<U32>, Maybe<&2, U32>, S.bsearch.array.find(_, n, key)) == ol : Array<U32>}
  %Equal.sym(Array<U32> & 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)) : {Pair.fst(Array<U32>, Maybe<&2, U32>, S.bsearch.array.found(U32.is_lt(r, n), _, r, key)) == ol : Array<U32>}
  ba.fs(U32.is_lt(r, n), ol, AR.Arrays.nth(U32, l, AR.Arrays.index(d, r), 0), r, key)

Uses (27):
  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=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_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.fst
  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=bend-osdev-algo@0.1.0.0/PROOF.bend&name=ba.fs
  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/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.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/array.bend&name=Arrays.index
  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