const ordinal : set prop const ordsucc : set set axiom ordinal_ordsucc: !x:set.ordinal x -> ordinal (ordsucc x) const SNo : set prop 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) -> x + ordsucc y = ordsucc (x + y) var x:set var y:set hyp ordinal x hyp ordinal y hyp SNo y claim SNo x -> x + ordsucc y = ordsucc (x + y)