const ordinal : set prop const SNo : set prop axiom ordinal_SNo: !x:set.ordinal x -> SNo x const ordsucc : set set const add_SNo : set set set term + = add_SNo infix + 2281 2280 lemma !x:set.!y:set.ordinal x -> ordinal y -> SNo y -> SNo x -> ordinal (ordsucc y) -> SNo (ordsucc y) -> x + ordsucc y = ordsucc (x + y) var x:set var y:set hyp ordinal x hyp ordinal y hyp SNo y hyp SNo x claim ordinal (ordsucc y) -> x + ordsucc y = ordsucc (x + y)