const CSNo : set prop const SNo : set prop const CSNo_Im : set set axiom CSNo_ImR: !x:set.CSNo x -> SNo (CSNo_Im x) const mul_CSNo : set set set const CSNo_Re : set set lemma !x:set.!y:set.CSNo x -> CSNo y -> CSNo (mul_CSNo x y) -> CSNo (mul_CSNo y x) -> SNo (CSNo_Re x) -> SNo (CSNo_Re y) -> SNo (CSNo_Im x) -> SNo (CSNo_Im y) -> mul_CSNo x y = mul_CSNo y x var x:set var y:set hyp CSNo x hyp CSNo y hyp CSNo (mul_CSNo x y) hyp CSNo (mul_CSNo y x) hyp SNo (CSNo_Re x) hyp SNo (CSNo_Re y) claim SNo (CSNo_Im x) -> mul_CSNo x y = mul_CSNo y x