def odd_value

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/w64add.bend:202

import Base
import bend-collections-laws-math@1.0.0.0/spec/math/w64.bend as SW
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u32laws.bend as LW

202def odd_value(+a: WU.U64) -> SW.Odd.value(a):
203  match a:
204    case WU.U64{+l, +h}:
205      Equal.trans(Bool, U32.is_eq(U32.and(l, 1), 1), Nat.is_eq(Nat.mod(v(l), 2n), 1n), Nat.is_eq(Nat.mod(val(l, h), 2n), 1n), LW.tests_odd(l), Equal.cong(Nat, Bool, t => Nat.is_eq(t, 1n), Nat.mod(v(l), 2n), Nat.mod(val(l, h), 2n), Equal.sym(Nat, Nat.mod(val(l, h), 2n), Nat.mod(v(l), 2n), WW.odd_limb(31n, v(l), v(h)))))