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 SNoLt : set set prop term < = SNoLt infix < 2020 2020 axiom ordinal_In_SNoLt: !x:set.ordinal x -> !y:set.y iIn x -> y < x const add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom add_SNo_Lt1: !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> x < z -> (x + y) < z + y axiom ordinal_SNoLt_In: !x:set.!y:set.ordinal x -> ordinal y -> x < y -> x iIn y var x:set var y:set var z:set hyp ordinal x hyp ordinal y hyp z iIn x hyp ordinal z hyp ordinal (x + y) claim ordinal (z + y) -> z + y iIn x + y