law le_min

bend-mathlib@0.8.1.0 · nat.bend:2456

import Base

2456# 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).
2457law le_min:
2458  for a: Nat
2459  for b: Nat
2460  for c: Nat
2461  {Nat.is_le(a, Nat.min(b, c)) == Bool.and(Nat.is_le(a, b), Nat.is_le(a, c)) : Bool}