const In : set set prop term iIn = In infix iIn 2000 2000 term Subq = \x:set.\y:set.!z:set.z iIn x -> z iIn y const add_SNo : set set set term + = add_SNo infix + 2281 2280 const mul_SNo : set set set term * = mul_SNo infix * 2291 2290 const minus_SNo : set set term - = minus_SNo claim !x:set.!y:set.!z:set.!w:set.!u:set.!v:set.!x2:set.!y2:set.(!z2:set.z2 iIn x2 -> !P:prop.(!w2:set.w2 iIn z -> !u2:set.u2 iIn w -> z2 = w2 * y + x * u2 + - w2 * u2 -> P) -> (!w2:set.w2 iIn u -> !u2:set.u2 iIn v -> z2 = w2 * y + x * u2 + - w2 * u2 -> P) -> P) -> (!z2:set.z2 iIn z -> !w2:set.w2 iIn w -> z2 * y + x * w2 + - z2 * w2 iIn y2) -> (!z2:set.z2 iIn u -> !w2:set.w2 iIn v -> z2 * y + x * w2 + - z2 * w2 iIn y2) -> !z2:set.z2 iIn x2 -> z2 iIn y2