const bij : set set (set set) prop term equip = \x:set.\y:set.?f:set set.bij x y f const In : set set prop term iIn = In infix iIn 2000 2000 const omega : set term finite = \x:set.?y:set.y iIn omega & equip x y 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 Sing : set set var x:set var y:set hyp finite x hyp y iIn x claim binunion x (Sing y) = x -> finite (binunion x (Sing y))