const SNo : set prop const minus_SNo : set set term - = minus_SNo axiom SNo_minus_SNo: !x:set.SNo x -> SNo - x const SNoLe : set set prop term <= = SNoLe infix <= 2020 2020 const add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom add_SNo_Le1: !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> x <= z -> (x + y) <= z + y const Empty : set axiom add_SNo_minus_SNo_rinv: !x:set.SNo x -> x + - x = Empty const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const abs_SNo : set set lemma !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> x <= y -> y < x + z -> Empty <= y + - x -> abs_SNo (y + - x) < z claim !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> x <= y -> y < x + z -> abs_SNo (y + - x) < z