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