(* First assignment for the course G54DTP. *)
(* Venanzio Capretta, February 2011. *)
(* Complete the proofs, 1 point each. *)
Variables A B C D: Prop.
Lemma ex1:
(A->B->C) -> B -> A -> C.
Proof.
?
Qed.
Lemma ex2:
(A->B) -> (A-> B->C) -> A -> C.
Proof.
?
Qed.
Lemma ex3:
(A/\B -> C) -> (A->B) -> A -> C.
Proof.
?
Qed.
Lemma ex4:
(A->B) -> (C->D) -> A\/C -> B\/D.
Proof.
?
Qed.
Lemma ex5:
A\/(B/\C) -> (A\/B)/\(A\/C).
Proof.
?
Qed.
Lemma ex6:
(A->~B) -> B -> ~A.
Proof.
?
Qed.
Lemma ex7:
~(A\/B) -> ~A/\~B.
Proof.
?
Qed.
Lemma ex8:
~A\/~B -> ~(A/\B).
Proof.
?
Qed.
Lemma ex9:
~(A->B) -> ~B.
Proof.
?
Qed.
Lemma ex10:
~~(A\/~A).
Proof.
?
Qed.