Nat.add_left_cancel_iff_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 4855-4860 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=4855&end_line=4860

import Base

# Adding the same amount on the left does not change the equality test: a = b tests as k + a = k + b, reversed to rewrite toward the simple side.
law add_left_cancel_iff_sym:
  for k: Nat
  for -a: Nat
  for -b: Nat
  {Nat.is_eq(Nat.add(k, a), Nat.add(k, b)) == Nat.is_eq(a, b) : Bool}

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=add_left_cancel_iff