def eq_value

bend-collections-laws-crypto@1.0.0.0 · proofs/math/typed/w64add.bend:174

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

174def eq_value(+a: WU.U64, +b: WU.U64) -> SW.Eq.value(a, b):
175  match a b:
176    case WU.U64{+al, +ah} WU.U64{+bl, +bh}:
177      +e1 = Equal.trans(Bool, Bool.and(U32.is_eq(al, bl), U32.is_eq(ah, bh)), Bool.and(Nat.is_eq(v(al), v(bl)), U32.is_eq(ah, bh)), Bool.and(Nat.is_eq(v(al), v(bl)), Nat.is_eq(v(ah), v(bh))), Equal.cong(Bool, Bool, t => Bool.and(t, U32.is_eq(ah, bh)), U32.is_eq(al, bl), Nat.is_eq(v(al), v(bl)), LW.eq_nat(al, bl)), Equal.cong(Bool, Bool, t => Bool.and(Nat.is_eq(v(al), v(bl)), t), U32.is_eq(ah, bh), Nat.is_eq(v(ah), v(bh)), LW.eq_nat(ah, bh)))
178      Equal.trans(Bool, Bool.and(U32.is_eq(al, bl), U32.is_eq(ah, bh)), Bool.and(Nat.is_eq(v(al), v(bl)), Nat.is_eq(v(ah), v(bh))), Nat.is_eq(val(al, ah), val(bl, bh)), e1, WW.eq_limbs(32n, v(al), v(ah), v(bl), v(bh), vb(al), vb(bl)))