const SNo : set prop const add_SNo : set set set term + = add_SNo infix + 2281 2280 const minus_SNo : set set term - = minus_SNo axiom add_SNo_minus_R2: !x:set.!y:set.SNo x -> SNo y -> (x + y) + - y = x const SNoLt : set set prop term < = SNoLt infix < 2020 2020 lemma !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> (x + y) < z + y -> (x + y) + - y = x -> (z + y) + - y = z -> x < z var x:set var y:set var z:set hyp SNo x hyp SNo y hyp SNo z hyp (x + y) < z + y claim (x + y) + - y = x -> x < z