ProofNat.le_sub_r: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_nat.bend as ProofNat
Lines 1535-1541 of lawful-words@0.1.0.0/proof_nat.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_nat.bend&start_line=1535&end_line=1541

import Base

# a + c <= x gives c <= x - a.
law le_sub_r:
  for +a: Nat
  for +c: Nat
  for +x: Nat
  for +h: {Nat.is_le(Nat.add(a, c), x) == True{} : Bool}
  {Nat.is_le(c, Nat.sub(x, a)) == True{} : Bool}

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=Empty.absurd
  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_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=false_ne_true
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=sub_zero