PAThm06Ind
Premises:
(forall (?X ?Y ?Z) (= (* ?X (+ ?Y ?Z)) (+ (* ?X ?Y) (* ?X ?Z)))) (forall (?X ?Y ?Z) (= (* (+ ?Y ?Z) ?X) (+ (* ?Y ?X) (* ?Z ?X)))) (forall (?X ?Y) (= (+ ?X (succ ?Y)) (succ (+ ?X ?Y)))) (forall ?X (= ?X (* (succ 0) ?X))) (forall ?X (= ?X (* ?X (succ 0)))) (forall ?X (= (succ ?X) (+ ?X (succ 0))))
Conclusion:
(forall (?X ?Y) (= (* (succ ?X) ?Y) (+ (* ?X ?Y) ?Y)))