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ACL2 !>(defun app (x y) (cond ((endp x) y) (t (cons (car x) (app (cdr x) y))))) The admission of APP is trivial, using the relation O< (which is known to be well-founded on the domain recognized by O-P ) and the measure (ACL2-COUNT X). We observe that the type of APP is described by the theorem (OR (CONSP (APP X Y)) (EQUAL (APP X Y) Y)). We used primitive type reasoning. Summary Form: ( DEFUN APP ...) Rules: ((:FAKE-RUNE-FOR-TYPE-SET NIL)) Warnings: None Time: 0.03 seconds (prove: 0.00, print: 0.00, other: 0.03) APP