const In : set set prop term iIn = In infix iIn 2000 2000 term nIn = \x:set.\y:set.~ x iIn y const bij : set set (set set) prop term equip = \x:set.\y:set.?f:set set.bij x y f const Empty : set axiom EmptyE: !x:set.nIn x Empty axiom FalseE: ~ False axiom bijE: !x:set.!y:set.!f:set set.bij x y f -> !P:prop.((!z:set.z iIn x -> f z iIn y) -> (!z:set.z iIn x -> !w:set.w iIn x -> f z = f w -> z = w) -> (!z:set.z iIn y -> ?w:set.w iIn x & f w = z) -> P) -> P axiom Empty_eq: !x:set.(!y:set.nIn y x) -> x = Empty claim !x:set.equip x Empty -> x = Empty