Nat.le_and_le_sub_iff_add_le_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 4311-4316 of bend-mathlib@0.8.1.0/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/nat.bend&start_line=4311&end_line=4316

import Base

# A sum is at most c exactly when a <= c and b <= c - a: a + b <= c tests as both, reversed to rewrite toward the simple side.
law le_and_le_sub_iff_add_le_sym:
  for a: Nat
  for -b: Nat
  for c: Nat
  {Nat.is_le(Nat.add(a, b), c) == Bool.and(Nat.is_le(a, c), Nat.is_le(b, Nat.sub(c, a))) : Bool}

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=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_and_le_sub_iff_add_le