(* 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.