Nat.add_le_add_iff_left: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 1514-1519 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=1514&end_line=1519

import Base

# Adding the same amount on the left does not change the order test: a <= b tests as k + a <= k + b.
law add_le_add_iff_left:
  for k: Nat
  for -a: Nat
  for -b: Nat
  {Nat.is_le(a, b) == Nat.is_le(Nat.add(k, a), Nat.add(k, b)) : Bool}

Uses (4):
  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_le