The Induction Scheme Selected for the App Example

   (IMPLIES (AND (NOT (ENDP A))         ; Induction Step: test 
                 (:P (CDR A) B C))      ;  and induction hypothesis
            (:P A B C))                 ;  implies induction conclusion.
   (IMPLIES (ENDP A) (:P A B C)))       ; Base Case 

The formula beginning with this parenthesis is the induction scheme suggested by (APP A B) applied to (P A B C).

It is a conjunction (AND ) of two formulas.

The first is the induction step and the second is the base case.