def ba.fl.body

bend-osdev-algo@0.1.0.0 · PROOF.bend:1453

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

1453def ba.fl.body(+d: Nat, -a: Array<U32>, +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<U32>}, +hl: {List.length(&2, U32, l) == AR.Arrays.slots(d) : Nat}) -> {Laws.algo_index_nat(Pair.snd(Array<U32>, 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>}:
1454  -ol = AR.Arrays.of_list(U32, d, l, 0)
1455  +r = Q.bq.run(33n, d, l, 0, n, key)
1456  %e1 : {Laws.algo_index_nat(Pair.snd(Array<U32>, 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>}
1457  %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<U32>, 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>}
1458  %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)) : {Laws.algo_index_nat(Pair.snd(Array<U32>, Maybe<&2, U32>, S.bsearch.array.find(_, n, key))) == S.bsearch.find(Q.bq.pre(l, n), key) : Maybe<&2, Nat>}
1459  %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)) : {Laws.algo_index_nat(Pair.snd(Array<U32>, 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>}
1460  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)))