PROOF.ud.dz2: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 1811-1814 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=1811&end_line=1814

import Base

def ud.dz2(+aw: Word(32n), +bw: Word(32n), G: Word(32n) & U32, iv: {Nat.add(Nat.mul(ud.q(32n, G), U32.to_nat(U32{bw})), ud.r(32n, G)) == Word.to_nat(32n, aw) : Nat} & {Nat.is_lt(ud.r(32n, G), U32.to_nat(U32{bw})) == True{} : Bool}) -> {Nat.add(Nat.mul(U32.to_nat(U32.div.fin(G)), Word.to_nat(32n, bw)), U32.to_nat(U32.mod.fin(G))) == Word.to_nat(32n, aw) : Nat} & {Nat.is_lt(U32.to_nat(U32.mod.fin(G)), Word.to_nat(32n, bw)) == True{} : Bool}:
  match G:
    case (q, r):
      iv

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Sigma
  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.fin
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.mod.fin
  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.q
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=ud.r