const SNo_pair : set set set const add_SNo : set set set term + = add_SNo infix + 2281 2280 const CSNo_Re : set set const CSNo_Im : set set term add_CSNo = \x:set.\y:set.SNo_pair (CSNo_Re x + CSNo_Re y) (CSNo_Im x + CSNo_Im y) const CSNo : set prop const SNo : set prop axiom CSNo_ReR: !x:set.CSNo x -> SNo (CSNo_Re x) axiom SNo_add_SNo: !x:set.!y:set.SNo x -> SNo y -> SNo (x + y) axiom CSNo_ImR: !x:set.CSNo x -> SNo (CSNo_Im x) axiom CSNo_I: !x:set.!y:set.SNo x -> SNo y -> CSNo (SNo_pair x y) claim !x:set.!y:set.CSNo x -> CSNo y -> CSNo (add_CSNo x y)