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 term TransSet = \x:set.!y:set.y iIn x -> Subq y x const SNo : set prop const SNoLe : set set prop term <= = SNoLe infix <= 2020 2020 term SNo_max_of = \x:set.\y:set.y iIn x & SNo y & !z:set.z iIn x -> SNo z -> z <= y const SNoLt : set set prop term < = SNoLt infix < 2020 2020 axiom SNoLtLe_tra: !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> x < y -> y <= z -> x < z axiom SNoLt_irref: !x:set.~ x < x const SNoLev : set set const SNoL : set set var x:set var y:set var z:set hyp SNo x hyp SNo y hyp !w:set.w iIn SNoL x -> SNo w -> w <= y hyp SNoLev y iIn SNoLev x hyp SNo z hyp SNoLev z iIn SNoLev y hyp y < z hyp z < x claim z iIn SNoL x -> x <= z