const In : set set prop term iIn = In infix iIn 2000 2000 term bij = \x:set.\y:set.\f:set set.(!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 const Eps_i : (set prop) set term inv = \x:set.\f:set set.\y:set.Eps_i \z:set.z iIn x & f z = y axiom inj_linv: !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 var x:set var y:set var f:set set var z:set hyp !w:set.w iIn x -> f w iIn y hyp !w:set.w iIn x -> !u:set.u iIn x -> f w = f u -> w = u hyp z iIn x claim f z iIn y -> ?w:set.w iIn y & Eps_i (\u:set.u iIn x & f u = w) = z