Library Stdlib.ZArith.Zmin

From Stdlib Require Import BinInt Zcompare Zorder.

#[local] Open Scope Z_scope.

Lemma Zmin_spec x y :
  x <= y /\ Z.min x y = x \/ x > y /\ Z.min x y = y.

Lemma Zmin_irreducible n m : Z.min n m = n \/ Z.min n m = m.


Lemma Zmin_le_prime_inf n m p : Z.min n m <= p -> {n <= p} + {m <= p}.

Lemma Zpos_min_1 p : Z.min 1 (Zpos p) = 1.