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+Definition trois := 3. (*test-definition*)
+Print trois.
+Eval compute in 10 * trois * trois.
+
+
+
+Lemma easy_proof : forall A : Prop, A -> A.
+Proof using .
+ intros A.
+ intros proof_of_A. (*test-insert*)
+ exact proof_of_A.
+Qed. (*test-lemma*)
+
+Lemma false_proof : forall A B : bool, A = B.
+Proof.
+ intros A B.
+ destruct A.
+ destruct B.
+ reflexivity. (*error*)
+ reflexivity.
+Qed. (*test-lemma2*)
+