The_Induction_Step_in_the_App_Example.html -- ACL2 Version 6.3

## The Induction Step in the App Example

This formula is the Induction Step. It basically consists of three parts, a test identifying the inductive case, an induction hypothesis and an induction conclusion.

    (IMPLIES (AND (NOT (ENDP A))      ; Test
                  (:P (CDR A) B C))   ; Induction Hypothesis
             (:P A B C))              ; Induction Conclusion

When we prove this we can assume

      * A is not empty, and that

      * the associativity conjecture holds for a ``smaller'' version of
        A, namely, (CDR A).

Under those hypotheses we have to prove the associativity conjecture for `A` itself.