Lemmas.and_le_sub: law of bend-kit-lemmas@0.1.1.0
Import: import bend-kit-lemmas@0.1.1.0/lemmas.bend as Lemmas
Lines 709-717 of bend-kit-lemmas@0.1.1.0/lemmas.bend: https://jend.leeeet.dev/read.txt?path=bend-kit-lemmas@0.1.1.0/lemmas.bend&start_line=709&end_line=717

import Base
import bend-mathlib@0.7.4.0/nat.bend as MNat

law and_le_sub:
  for c: Bool
  for +a: Nat
  for +b: Nat
  for +l: Nat
  for -s: Nat
  for +hc: {Nat.is_le(a, l) == c : Bool}
  for hs: MNat.le(a, l) -> {s == Nat.sub(l, a) : Nat}
  {Bool.and(c, Nat.is_le(b, s)) == Nat.is_le(Nat.add(a, b), l) : 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=Bool.and
  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-mathlib@0.8.1.0/nat.bend&name=le
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=le_and_le_sub_iff_add_le