+
+
+(* this test shows what happens when a term of type A -> ? is applied to
+ a goal of type A' -> B: if A unifies with A' the unifier becomes ? := B
+ and no goal is opened; otherwise the unifier becomes ? := A' -> B and a
+ new goal of type A is created. *)
+theorem c:
+ \forall A,B:Prop.
+ 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.
+
+(* 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.
\ No newline at end of file