ProofCut.lt_sub_of: law of lawful-fields@0.1.1.0
Import: import lawful-fields@0.1.1.0/proof_cut.bend as ProofCut
Lines 91-97 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=91&end_line=97

import Base

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

Uses (12):
  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=Equal.trans
  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.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=add_succ
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_sub_r
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_succ_lt