const In : set set prop term iIn = In infix iIn 2000 2000 const real : set const minus_SNo : set set term - = minus_SNo axiom real_minus_SNo: !x:set.x iIn real -> - x iIn real const SNo : set prop axiom real_SNo: !x:set.x iIn real -> SNo x const mul_SNo : set set set term * = mul_SNo infix * 2291 2290 axiom mul_SNo_minus_distrL: !x:set.!y:set.SNo x -> SNo y -> (- x) * y = - x * y axiom mul_SNo_minus_distrR: !x:set.!y:set.SNo x -> SNo y -> x * - y = - x * y const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const Empty : set const ordsucc : set set axiom pos_real_recip_ex: !x:set.x iIn real -> Empty < x -> ?y:set.y iIn real & x * y = ordsucc Empty var x:set hyp x iIn real hyp SNo x hyp x < Empty claim Empty < - x -> ?y:set.y iIn real & x * y = ordsucc Empty