MapDifferenceOrder.add_complement: law of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/map_difference_order.bend as MapDifferenceOrder
Lines 52-56 of bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/map_difference_order.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/map_difference_order.bend&start_line=52&end_line=56

import Base

law add_complement:
  for n: Nat
  for m: Nat
  for bound: {Nat.is_le(m, n) == True{} : Bool}
  {Nat.add(m, Nat.sub(n, m)) == n : Nat}

Uses (8):
  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.cong
  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=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/map_routing.bend&name=false_true