const SNo : set prop const Empty : set axiom SNo_0: SNo Empty const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const mul_SNo : set set set term * = mul_SNo infix * 2291 2290 axiom mul_SNo_neg_neg: !x:set.!y:set.SNo x -> SNo y -> x < Empty -> y < Empty -> Empty < x * y axiom mul_SNo_pos_pos: !x:set.!y:set.SNo x -> SNo y -> Empty < x -> Empty < y -> Empty < x * y axiom SNoLt_trichotomy_or_impred: !x:set.!y:set.SNo x -> SNo y -> !P:prop.(x < y -> P) -> (x = y -> P) -> (y < x -> P) -> P claim !x:set.SNo x -> x = Empty | Empty < x * x