Fact.sub_sub_self: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/fact.bend as Fact
Lines 219-224 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/fact.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/fact.bend&start_line=219&end_line=224

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as A

# n - (n - k) == k for k <= n
def sub_sub_self(+n: Nat, +k: Nat, +h: {Nat.is_le(k, n) == True{} : Bool}) -> {Nat.sub(n, Nat.sub(n, k)) == k : Nat}:
  +e = N.sub_add(n, k, h)
  %Equal.sym(Nat, n, Nat.add(k, Nat.sub(n, k)), Equal.sym(Nat, Nat.add(k, Nat.sub(n, k)), n, e)) : {Nat.sub(_, Nat.sub(n, k)) == k : Nat}
  %Equal.sym(Nat, Nat.add(k, Nat.sub(n, k)), Nat.add(Nat.sub(n, k), k), A.add_comm(k, Nat.sub(n, k))) : {Nat.sub(_, Nat.sub(n, k)) == k : Nat}
  N.add_sub_cancel(Nat.sub(n, k), k)

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=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=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_comm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=add_sub_cancel
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=sub_add