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 Sing : set set axiom SingI: !x:set.x iIn Sing x const ordsucc : set set axiom ordsuccE: !x:set.!y:set.y iIn ordsucc x -> y iIn x | y = x claim !x:set.x iIn ordsucc Empty -> x iIn Sing Empty