ProofWord.carry_mod: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_word.bend as ProofWord
Lines 146-154 of lawful-words@0.1.0.0/proof_word.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_word.bend&start_line=146&end_line=154

import Base

# r + c * m = x with r < m gives x % m = r.
law carry_mod:
  for +r: Nat
  for +c: Nat
  for +m: Nat
  for +x: Nat
  for +e: {Nat.add(r, Nat.mul(c, m)) == x : Nat}
  for +h: {Nat.is_lt(r, m) == True{} : Bool}
  {Nat.mod(x, m) == r : Nat}

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=add_comm
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mod_mul_add