Nat.le_max_iff_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 4718-4723 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=4718&end_line=4723

import Base

# A number is at most the maximum exactly when it is at most one argument: a <= max b c tests as a <= b or a <= c, reversed to rewrite toward the simple side.
law le_max_iff_sym:
  for a: Nat
  for b: Nat
  for c: Nat
  {Bool.or(Nat.is_le(a, b), Nat.is_le(a, c)) == Nat.is_le(a, Nat.max(b, c)) : Bool}

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.or
  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.max
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=le_max_iff