Overview_of_the_Simplification_of_the_Induction_Step_to_T.html -- ACL2 Version 6.3

## Overview of the Simplification of the Induction Step to T

    Subgoal *1/2
    (IMPLIES (AND (NOT (ENDP A))
                  (EQUAL (APP (APP (CDR A) B) C)
                         (APP (CDR A) (APP B C))))
             (EQUAL (APP (APP A B) C)
                    (APP A (APP B C)))).

    By the simple :definition ENDP we reduce the conjecture to

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

    But simplification reduces this to T, using the :definition APP, the
    :rewrite rules CDR-CONS and CAR-CONS and primitive type reasoning.