W64add.mcons: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend as W64add
Lines 339-340 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend&start_line=339&end_line=340

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64mul.bend as W64M

def mcons(+x: U32, +y: U32) -> {Nat.add(v(U32.mul(x, y)), C.shift(32n, W64M.mex(x, y))) == Nat.mul(v(x), v(y)) : Nat}:
  Equal.trans(Nat, Nat.add(v(U32.mul(x, y)), C.shift(32n, W64M.mex(x, y))), Nat.add(v(U32.mul(x, y)), WD.sc(32n, W64M.mex(x, y))), Nat.mul(v(x), v(y)), Equal.cong(Nat, Nat, z => Nat.add(v(U32.mul(x, y)), z), C.shift(32n, W64M.mex(x, y)), WD.sc(32n, W64M.mex(x, y)), W64M.shift_sc(32n, W64M.mex(x, y))), W64M.mul_cons(x, y))

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend&name=sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64mul.bend&name=mex
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64mul.bend&name=mul_cons
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64mul.bend&name=shift_sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=shift