The_Simplification_of_the_Induction_Conclusion__lparen_Step_8_rparen_.html -- ACL2 Version 6.3

## the Simplification of the Induction Conclusion (Step 8)

    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))
                    (APP A (APP B C)))).

Click on the link above to expand the definition of `APP` here. This time, we'll do the whole expansion at once, including the simplification of the resulting `IF`. This is how ACL2 actually does it.