def lt_value

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/w64add.bend:180

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/lib/u32.bend as U3
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

180def lt_value(+a: WU.U64, +b: WU.U64) -> SW.Lt.value(a, b):
181  match a b:
182    case WU.U64{+al, +ah} WU.U64{+bl, +bh}:
183      +x = Bool.or(U32.is_lt(ah, bh), Bool.and(U32.is_eq(ah, bh), U32.is_lt(al, bl)))
184      +y1 = Bool.or(Nat.is_lt(v(ah), v(bh)), Bool.and(U32.is_eq(ah, bh), U32.is_lt(al, bl)))
185      +y2 = Bool.or(Nat.is_lt(v(ah), v(bh)), Bool.and(Nat.is_eq(v(ah), v(bh)), U32.is_lt(al, bl)))
186      +y3 = Bool.or(Nat.is_lt(v(ah), v(bh)), Bool.and(Nat.is_eq(v(ah), v(bh)), Nat.is_lt(v(al), v(bl))))
187      +e1 = Equal.cong(Bool, Bool, t => Bool.or(t, Bool.and(U32.is_eq(ah, bh), U32.is_lt(al, bl))), U32.is_lt(ah, bh), Nat.is_lt(v(ah), v(bh)), U3.is_lt_nat(ah, bh))
188      +e2 = Equal.cong(Bool, Bool, t => Bool.or(Nat.is_lt(v(ah), v(bh)), Bool.and(t, U32.is_lt(al, bl))), U32.is_eq(ah, bh), Nat.is_eq(v(ah), v(bh)), LW.eq_nat(ah, bh))
189      +e3 = Equal.cong(Bool, Bool, t => Bool.or(Nat.is_lt(v(ah), v(bh)), Bool.and(Nat.is_eq(v(ah), v(bh)), t)), U32.is_lt(al, bl), Nat.is_lt(v(al), v(bl)), U3.is_lt_nat(al, bl))
190      Equal.trans(Bool, x, y1, Nat.is_lt(val(al, ah), val(bl, bh)), e1, Equal.trans(Bool, y1, y2, Nat.is_lt(val(al, ah), val(bl, bh)), e2, Equal.trans(Bool, y2, y3, Nat.is_lt(val(al, ah), val(bl, bh)), e3, WW.lt_limbs(32n, v(al), v(ah), v(bl), v(bh), vb(al), vb(bl)))))