const In : set set prop term iIn = In infix iIn 2000 2000 const SNo : set prop const SNoLt : set set prop term < = SNoLt infix < 2020 2020 term SNoCutP = \x:set.\y:set.(!z:set.z iIn x -> SNo z) & (!z:set.z iIn y -> SNo z) & !z:set.z iIn x -> !w:set.w iIn y -> z < w const SNoCut : set set set axiom SNoCutP_SNoCut_R: !x:set.!y:set.SNoCutP x y -> !z:set.z iIn y -> SNoCut x y < z const minus_SNo : set set term - = minus_SNo axiom minus_SNo_Lt_contra: !x:set.!y:set.SNo x -> SNo y -> x < y -> - y < - x var x:set var y:set var z:set hyp SNoCutP x y hyp SNo (SNoCut x y) hyp SNo - SNoCut x y hyp z iIn y hyp SNo z claim SNo - z -> - - SNoCut x y < - - z