const ordinal : set prop const add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom add_SNo_ordinal_ordinal: !x:set.ordinal x -> !y:set.ordinal y -> ordinal (x + y) const In : set set prop term iIn = In infix iIn 2000 2000 lemma !x:set.!y:set.!z:set.ordinal x -> ordinal y -> z iIn x -> ordinal z -> ordinal (x + y) -> z + y iIn x + y var x:set var y:set var z:set hyp ordinal x hyp ordinal y hyp z iIn x claim ordinal z -> z + y iIn x + y