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 term Subq = \x:set.\y:set.!z:set.z iIn x -> z iIn y term nIn = \x:set.\y:set.~ x iIn y const binunion : set set set const Empty : set axiom binunion_idr: !x:set.binunion x Empty = x const famunion : set (set set) set axiom famunion_Empty: !f:set set.famunion Empty f = Empty const Sing : set set const ordsucc : set set const SNoLev : set set const Repl : set (set set) set const eps_ : set set var x:set hyp famunion (Sing Empty) (\y:set.ordsucc (SNoLev y)) = ordsucc Empty hyp x = Empty claim Repl x eps_ = Empty -> binunion (famunion (Sing Empty) \y:set.ordsucc (SNoLev y)) (famunion (Repl x eps_) \y:set.ordsucc (SNoLev y)) = ordsucc x