U64div.mul32: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64div.bend as U64div
Lines 42-47 of bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64div.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64div.bend&start_line=42&end_line=47

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend as UD

def mul32(+one: Nat, +h1: {one == 1n : Nat}, +x: U32, +y: U32, +h: {Nat.is_lt(Nat.mul(UD.v(x), UD.v(y)), WD.sc(32n, one)) == True{} : Bool}) -> {UD.v(U32.mul(x, y)) == Nat.mul(UD.v(x), UD.v(y)) : Nat}:
  match x y:
    case U32{+a} U32{+b}:
      +cv = Equal.trans(Nat, Nat.mul(UD.v(U32{a}), UD.v(U32{b})), Nat.mul(WD.uw(32n, a), UD.v(U32{b})), Nat.mul(WD.uw(32n, a), WD.uw(32n, b)), Equal.cong(Nat, Nat, z => Nat.mul(z, UD.v(U32{b})), UD.v(U32{a}), WD.uw(32n, a), UD.vw(a)), Equal.cong(Nat, Nat, z => Nat.mul(WD.uw(32n, a), z), UD.v(U32{b}), WD.uw(32n, b), UD.vw(b)))
      +hw = L.subst(Nat, z => {Nat.is_lt(z, WD.sc(32n, one)) == True{} : Bool}, Nat.mul(UD.v(U32{a}), UD.v(U32{b})), Nat.mul(WD.uw(32n, a), WD.uw(32n, b)), cv, h)
      Equal.trans(Nat, UD.v(U32{Word.mul(32n, a, b)}), WD.uw(32n, Word.mul(32n, a, b)), Nat.mul(UD.v(U32{a}), UD.v(U32{b})), UD.vw(Word.mul(32n, a, b)), Equal.trans(Nat, WD.uw(32n, Word.mul(32n, a, b)), Nat.mul(WD.uw(32n, a), WD.uw(32n, b)), Nat.mul(UD.v(U32{a}), UD.v(U32{b})), WD.mul_exact(32n, one, h1, a, b, hw), Equal.sym(Nat, Nat.mul(UD.v(U32{a}), UD.v(U32{b})), Nat.mul(WD.uw(32n, a), WD.uw(32n, b)), cv)))

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.sym
  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.is_lt
  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=Base/base.bend&name=Word.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend&name=vw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=mul_exact
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=uw