Subgoal *1/1 (IMPLIES (ENDP A) (EQUAL (APP (APP A B) C) (APP A (APP B C)))). By the simple :definition ENDP we reduce the conjecture to Subgoal *1/1' (IMPLIES (NOT (CONSP A)) (EQUAL (APP (APP A B) C) (APP A (APP B C)))). But simplification reduces this to T, using the :definition APP and primitive type reasoning.