ProofBase.lt_sub: law of lawful-arrays@0.1.0.0
Import: import lawful-arrays@0.1.0.0/proof_base.bend as ProofBase
Lines 186-193 of lawful-arrays@0.1.0.0/proof_base.bend: https://jend.leeeet.dev/read.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&start_line=186&end_line=193

import Base

# k is at least m and below m + m2, so k - m is below m2.
law lt_sub:
  for +m: Nat
  for +k: Nat
  for +m2: Nat
  for h1: {Nat.is_lt(k, m) == False{} : Bool}
  for h2: {Nat.is_lt(k, Nat.add(m, m2)) == True{} : Bool}
  {Nat.is_lt(Nat.sub(k, m), m2) == 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_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=sub_zero
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=true_ne_false