Nat.sub_add_comm: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 3704-3710 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=3704&end_line=3710

import Base

# Subtracting from the left summand commutes with adding the right one: k <= n implies (n + m) - k = (n - k) + m.
law sub_add_comm:
  for n: Nat
  for m: Nat
  for k: Nat
  for h: le(k, n)
  {Nat.sub(Nat.add(n, m), k) == Nat.add(Nat.sub(n, k), m) : Nat}

Uses (6):
  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.sub
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=add_comm
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=add_sub_assoc
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=le