PROOF.ud.dz: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 1816-1821 of bend-osdev-u32@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&start_line=1816&end_line=1821

import Base

def ud.dz(+aw: Word(32n), +bw: Word(32n), z: Bool, ez: {U32.is_zero(U32{bw}) == z : Bool}, h: {U32.is_zero(U32{bw}) == False{} : Bool}) -> {Nat.add(Nat.mul(U32.to_nat(U32.div.if(aw, U32{bw}, z)), Word.to_nat(32n, bw)), U32.to_nat(U32.mod.if(aw, U32{bw}, z))) == Word.to_nat(32n, aw) : Nat} & {Nat.is_lt(U32.to_nat(U32.mod.if(aw, U32{bw}, z)), Word.to_nat(32n, bw)) == True{} : Bool}:
  match z:
    case True{}:
      Empty.absurd({Nat.add(Nat.mul(U32.to_nat(U32.div.if(aw, U32{bw}, True{})), Word.to_nat(32n, bw)), U32.to_nat(U32.mod.if(aw, U32{bw}, True{}))) == Word.to_nat(32n, aw) : Nat} & {Nat.is_lt(U32.to_nat(U32.mod.if(aw, U32{bw}, True{})), Word.to_nat(32n, bw)) == True{} : Bool}, un.tf(Equal.trans(Bool, True{}, U32.is_zero(U32{bw}), False{}, Equal.sym(Bool, U32.is_zero(U32{bw}), True{}, ez), h)))
    case False{}:
      ud.dz2(aw, bw, U32.divmod.go(32n, aw, U32{bw}), ud.go(32n, aw, U32{bw}, ud.hb(bw, h)))

Uses (21):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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.add
  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=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.div.if
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.divmod.go
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_zero
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.mod.if
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=ud.dz2
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=ud.go
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=ud.hb
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.tf