Nat.max_le: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 2480-2485 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=2480&end_line=2485

import Base

# The maximum is at most c exactly when both arguments are: max a b <= c tests as a <= c and b <= c (Mathlib's max_le_iff; the implication is max_le_of_le_of_le).
law max_le:
  for a: Nat
  for b: Nat
  for c: Nat
  {Nat.is_le(Nat.max(a, b), c) == Bool.and(Nat.is_le(a, c), Nat.is_le(b, c)) : Bool}

Uses (6):
  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=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.max
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=internal_and_true_sym