const SNoLe : set set prop term <= = SNoLe infix <= 2020 2020 axiom SNoLe_ref: !x:set.x <= x const SNo : set prop const minus_SNo : set set term - = minus_SNo const add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom minus_add_SNo_distr: !x:set.!y:set.SNo x -> SNo y -> - (x + y) = - x + - y const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const Empty : set const abs_SNo : set set axiom neg_abs_SNo: !x:set.SNo x -> x < Empty -> abs_SNo x = - x var x:set var y:set hyp SNo x hyp SNo y hyp SNo (x + y) hyp x < Empty hyp y < Empty claim (x + y) < Empty -> abs_SNo (x + y) <= - x + - y