const SNo : set prop const add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom SNo_add_SNo: !x:set.!y:set.SNo x -> SNo y -> SNo (x + y) const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const minus_SNo : set set term - = minus_SNo lemma !x:set.!y:set.!z:set.!w:set.!u:set.!v:set.SNo x -> SNo y -> SNo z -> SNo w -> SNo u -> SNo v -> (x + y + v) < w + u + z -> SNo - z -> SNo - v -> SNo (x + y) -> SNo (w + u) -> (x + y + - z) < w + u + - v var x:set var y:set var z:set var w:set var u:set var v:set hyp SNo x hyp SNo y hyp SNo z hyp SNo w hyp SNo u hyp SNo v hyp (x + y + v) < w + u + z hyp SNo - z hyp SNo - v claim SNo (x + y) -> (x + y + - z) < w + u + - v