proposition: Theorem contradiction_implies_anything : forall P Q : Prop, (P /\ ~P) -> Q.
proof: Proof. Admitted. Theorem double_neg : forall P : Prop, P -> ~~P. Proof. Admitted. Theorem not_true_is_false : forall b : bool, b <> true -> b = false. Proof. intros b H. destruct b eqn:HE. - unfold not in H. apply ex_falso_quodlibet. apply H. reflexivity. - reflexivity. Qed.