def ba.fls.body

bend-osdev-algo@0.1.0.0 · PROOF.bend:1467

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

1467def 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>}:
1468  -ol = AR.Arrays.of_list(U32, d, l, 0)
1469  +r = Q.bq.run(33n, d, l, 0, n, key)
1470  %e1 : {Pair.fst(Array<U32>, Maybe<&2, U32>, S.bsearch.array_find(_, n, key)) == _ : Array<U32>}
1471  %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>}
1472  %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>}
1473  ba.fs(U32.is_lt(r, n), ol, AR.Arrays.nth(U32, l, AR.Arrays.index(d, r), 0), r, key)