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+(* Some tests for contradiction *)
+
+Lemma L1 : forall A B : Prop, A -> ~A -> B.
+Proof.
+intros; contradiction.
+Qed.
+
+Lemma L2 : forall A B : Prop, ~A -> A -> B.
+Proof.
+intros; contradiction.
+Qed.
+
+Lemma L3 : forall A : Prop, ~True -> A.
+Proof.
+intros; contradiction.
+Qed.
+
+Lemma L4 : forall A : Prop, forall x : nat, ~x=x -> A.
+Proof.
+intros; contradiction.
+Qed.
+
+Lemma L5 : forall A : Prop, forall x y : nat, ~x=y -> x=y -> A.
+Proof.
+intros; contradiction.
+Qed.
+
+Lemma L6 : forall A : Prop, forall x y : nat, x=y -> ~x=y -> A.
+Proof.
+intros; contradiction.
+Qed.
+