const SNo : set prop const minus_SNo : set set term - = minus_SNo axiom SNo_minus_SNo: !x:set.SNo x -> SNo - x const mul_SNo : set set set term * = mul_SNo infix * 2291 2290 const add_SNo : set set set term + = add_SNo infix + 2281 2280 lemma !x:set.!y:set.!z:set.!w:set.SNo x -> SNo y -> SNo z -> SNo w -> SNo - y -> SNo - w -> (x + - y) * (z + - w) = x * z + - x * w + - y * z + y * w var x:set var y:set var z:set var w:set hyp SNo x hyp SNo y hyp SNo z hyp SNo w claim SNo - y -> (x + - y) * (z + - w) = x * z + - x * w + - y * z + y * w