Fact.sub_le_self: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/fact.bend as Fact
Lines 226-234 of bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/fact.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/fact.bend&start_line=226&end_line=234

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend as R

def sub_le_self(+n: Nat, +k: Nat) -> {Nat.is_le(Nat.sub(n, k), n) == True{} : Bool}:
  match n k:
    case 0n k0:
      %Equal.sym(Nat, Nat.sub(0n, k0), 0n, R.zsub(k0)) : {Nat.is_le(_, 0n) == True{} : Bool}
      {==}
    case 1n+ +np 0n:
      N.le_refl(1n+np)
    case 1n+ +np 1n+ +kp:
      N.le_trans(Nat.sub(np, kp), np, 1n+np, sub_le_self(np, kp), N.le_succ(np))

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.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-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_refl
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend&name=zsub