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