The_Simplification_of_the_Induction_Conclusion__lparen_Step_1_rparen_.html -- ACL2 Version 6.3

## the Simplification of the Induction Conclusion (Step 1)

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

Note that the `IF` expression above is the simplified body of `APP`. But we know the test `(CONSP A)` is true, by the first hypothesis. Click on the link above to replace the test by `T`. Actually this step and several subsequent ones are done during the simplification of the body of `APP` but we want to illustrate the basic principles of simplification without bothering with every detail.