Subgoal *1/2'
(IMPLIES (AND (CONSP A)
              (EQUAL (APP (APP (CDR A) B) C)
                     (APP (CDR A) (APP B C))))
         (EQUAL (IF (CONSP (CONS (CAR A) (APP (CDR A) B)))
                    (CONS (CAR (CONS (CAR A) (APP (CDR A) B)))
                          (APP (CDR (CONS (CAR A) (APP (CDR A) B)))
                               C))
                    C)
                (APP A (APP B C)))).

Click on the link above to apply the Axiom (CONSP (CONS x y)) = T.
 
 