The_Simplification_of_the_Induction_Conclusion__lparen_Step_9_rparen_.html -- ACL2 Version 6.3

## the Simplification of the Induction Conclusion (Step 9)

    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))`.