const SNo : set prop const add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom SNo_add_SNo: !x:set.!y:set.SNo x -> SNo y -> SNo (x + y) const mul_SNo : set set set term * = mul_SNo infix * 2291 2290 const eps_ : set set const ordsucc : set set const Empty : set lemma !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> x + x = y + z -> SNo (y + z) -> x = eps_ (ordsucc Empty) * (y + z) claim !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> x + x = y + z -> x = eps_ (ordsucc Empty) * (y + z)