proposition: Theorem contrapositive : forall (P Q : Prop), (P -> Q) -> (~Q -> ~P).
proof: Proof. Admitted. Theorem not_both_true_and_false : forall P : Prop, ~ (P /\ ~P). Proof. Admitted. Theorem not_true_is_false : forall b : bool, b <> true -> b = false. Proof. intros [] H. - unfold not in H. apply ex_falso_quodlibet. apply H. reflexivity. - reflexivity. Qed.
imports: Tactics