Nat.add_mul_mod_self_left_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 4758-4763 of bend-mathlib@0.8.1.0/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/nat.bend&start_line=4758&end_line=4763

import Base

# Adding a multiple of the divisor keeps the remainder: (a + b * c) % b = a % b, reversed to rewrite toward the simple side.
law add_mul_mod_self_left_sym:
  for a: Nat
  for b: Nat
  for c: Nat
  {Nat.mod(a, b) == Nat.mod(Nat.add(a, Nat.mul(b, c)), b) : Nat}

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=add_mul_mod_self_left