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The Simplification of the Induction Conclusion (Step 9)

The Simplification of the Induction Conclusion (Step 9)

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)) 
                (CONS (CAR A) 
                      (APP (CDR A) (APP B C))))). 

Click on the link above to apply the Axiom that (EQUAL (CONS x y) (CONS u v)) is equal to the conjunction of (EQUAL x u) and (EQUAL y v). In this case, (EQUAL x u) is trivial, (EQUAL (CAR A) (CAR A)).