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.