def ba.fl.ref

bend-osdev-algo@0.1.0.0 · PROOF.bend:1462

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-algo@0.1.0.0/LAWS.bend as Laws

1462def ba.fl.ref(+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}, r: &l: List<&2, U32> -> {AR.Arrays.of_list(U32, d, l, 0) == a : Array<U32>} & {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>}:
1463  (l, e) = r
1464  (e1, hl) = e
1465  ba.fl.body(d, a, hd, n, hn, key, hs, l, e1, hl)