Arith.sub_le2: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/arith.bend as Arith
Lines 168-177 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/arith.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/arith.bend&start_line=168&end_line=177

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

# a - b <= a
def sub_le2(+a: Nat, +b: Nat) -> {Nat.is_le(Nat.sub(a, b), a) == True{} : Bool}:
  match a b:
    case 0n _:
      %Equal.sym(Nat, Nat.sub(0n, b), 0n, zsub(b)) : {Nat.is_le(_, 0n) == True{} : Bool}
      {==}
    case 1n+p 0n:
      N.le_refl(1n+p)
    case 1n+p 1n+q:
      N.le_trans(Nat.sub(p, q), p, 1n+p, sub_le2(p, q), N.le_succ(p))

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/arith.bend&name=zsub
  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