const Eps_i : (set prop) set const In : set set prop term iIn = In infix iIn 2000 2000 term inv = \x:set.\f:set set.\y:set.Eps_i \z:set.z iIn x & f z = y axiom Eps_i_ax: !p:set prop.!x:set.p x -> p (Eps_i p) lemma !x:set.!f:set set.!y:set.(!z:set.z iIn x -> !w:set.w iIn x -> f z = f w -> z = w) -> y iIn x -> inv x f (f y) iIn x & f (inv x f (f y)) = f y -> inv x f (f y) = y claim !x:set.!f:set set.(!y:set.y iIn x -> !z:set.z iIn x -> f y = f z -> y = z) -> !y:set.y iIn x -> inv x f (f y) = y