const In : set set prop term iIn = In infix iIn 2000 2000 term nIn = \x:set.\y:set.~ x iIn y term Subq = \x:set.\y:set.!z:set.z iIn x -> z iIn y const Empty : set axiom EmptyE: !x:set.nIn x Empty axiom FalseE: ~ False const famunion : set (set set) set axiom famunionE_impred: !x:set.!f:set set.!y:set.y iIn famunion x f -> !P:prop.(!z:set.z iIn x -> y iIn f z -> P) -> P axiom Empty_Subq_eq: !x:set.Subq x Empty -> x = Empty claim !f:set set.famunion Empty f = Empty