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