law le_min_sym

bend-mathlib@0.8.1.0 · nat.bend:4561

import Base

4561# 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), reversed to rewrite toward the simple side.
4562law le_min_sym:
4563  for a: Nat
4564  for b: Nat
4565  for c: Nat
4566  {Bool.and(Nat.is_le(a, b), Nat.is_le(a, c)) == Nat.is_le(a, Nat.min(b, c)) : Bool}