A \to (\forall P: Prop. A \to P) \to (A \to B) \land (B \to B).
intros 4; split; [ apply H1 | apply H1; exact H ].
qed.
-
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+
+(* this test requires the delta-expansion of not in the type of the applied
+ term (to reveal a product) *)
+theorem d: \forall A: Prop. \lnot A \to A \to False.
+ intros. apply H. assumption.
+qed.
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