LAWS.nat_mod_unique: law of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/LAWS.bend as LAWS
Lines 380-389 of bend-osdev-u32@0.1.0.0/LAWS.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&start_line=380&end_line=389

import Base

law nat_mod_unique:
  for +b: Nat
  for +q1: Nat
  for +r1: Nat
  for +q2: Nat
  for +r2: Nat
  for e: {Nat.add(Nat.mul(q1, b), r1) == Nat.add(Nat.mul(q2, b), r2) : Nat}
  for h1: {Nat.is_lt(r1, b) == True{} : Bool}
  for h2: {Nat.is_lt(r2, b) == True{} : Bool}
  {r1 == r2 : Nat}

Uses (7):
  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=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.dmu
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.dmu.r