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 term ordinal = \x:set.TransSet x & !y:set.y iIn x -> TransSet y term nIn = \x:set.\y:set.~ x iIn y axiom In_no2cycle: !x:set.!y:set.x iIn y -> ~ y iIn x axiom In_irref: !x:set.nIn x x const ordsucc : set set axiom ordsuccE: !x:set.!y:set.y iIn ordsucc x -> y iIn x | y = x const SNoLev : set set const minus_SNo : set set term - = minus_SNo var x:set var y:set var z:set var w:set hyp y iIn ordsucc (SNoLev z) hyp z = - w hyp SNoLev w iIn SNoLev x hyp Subq (SNoLev - w) (SNoLev w) hyp Subq (SNoLev x) y claim ~ SNoLev w iIn y