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

Click on the link above to apply the Axiom that
(EQUAL (CONS x y) (CONS u v)) is equal to the conjunction of
(EQUAL x u) and (EQUAL y v).  In this case, (EQUAL x u)
is trivial, (EQUAL (CAR A) (CAR A)).
 
 