Nat.le_min: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 2456-2461 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=2456&end_line=2461

import Base

# A number is at most the minimum exactly when it is at most both: a <= min b c tests as a <= b and a <= c (Mathlib's le_min_iff; the implication is le_min_of_le_of_le).
law le_min:
  for a: Nat
  for b: Nat
  for c: Nat
  {Nat.is_le(a, Nat.min(b, c)) == Bool.and(Nat.is_le(a, b), Nat.is_le(a, 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.min
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=internal_and_false_sym