ProofCut.sub_le_of: law of lawful-fields@0.1.1.0
Import: import lawful-fields@0.1.1.0/proof_cut.bend as ProofCut
Lines 74-80 of lawful-fields@0.1.1.0/proof_cut.bend: https://jend.leeeet.dev/read.txt?path=lawful-fields@0.1.1.0/proof_cut.bend&start_line=74&end_line=80

import Base

# T <= s + r gives T - s <= r.
law sub_le_of:
  for +tt: Nat
  for +s: Nat
  for +r: Nat
  for +h: {Nat.is_le(tt, Nat.add(s, r)) == True{} : Bool}
  {Nat.is_le(Nat.sub(tt, s), r) == True{} : 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=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=le_zero_l