def is_zero

bend-collections-laws-math@1.0.0.0 · proofs/math/u64/u64.bend:150

import Base
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as U
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/src/wide.bend as W
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S

150# THEOREM: is_zero is the specification's zero test.
151def is_zero(+a: U.U64) -> {U.is_zero(a) == S.zero(bits(a)) : Bool}:
152  match a:
153    case U.U64{lo, hi}:
154      %Equal.sym(Word(64n), W.pack(0, 0), Word.zero(64n), zero_pack()) : {U.is_zero(U.U64{lo, hi}) == Cmp.is_eq(Word.cmp(64n, W.pack(lo, hi), _)) : Bool}
155      %Equal.sym(Cmp, Word.cmp(64n, W.pack(lo, hi), W.pack(0, 0)), U.order(U32.cmp(hi, 0), U32.cmp(lo, 0)), cmp_pack(lo, hi, 0, 0)) : {U.is_zero(U.U64{lo, hi}) == Cmp.is_eq(_) : Bool}
156      Equal.sym(Bool, Cmp.is_eq(U.order(U32.cmp(hi, 0), U32.cmp(lo, 0))), Bool.and(Cmp.is_eq(U32.cmp(lo, 0)), Cmp.is_eq(U32.cmp(hi, 0))), eq_order(U32.cmp(hi, 0), U32.cmp(lo, 0)))