proposition: Theorem iff_refl : forall P : Prop, P <-> P.
proof: Proof. MProof. Admitted. Theorem iff_trans : forall P Q R : Prop, (P <-> Q) -> (Q <-> R) -> (P <-> R). MProof. Admitted. Theorem or_distributes_over_and : forall P Q R : Prop, P \/ (Q /\ R) <-> (P \/ Q) /\ (P \/ R). MProof. Admitted. Require Import Coq.Setoids.Setoid. Lemma mult_0 : forall n m, n * m = 0 <-> n = 0 \/ m = 0. MProof. intros. T.split. - apply mult_eq_0. - apply or_example. Qed.