const setsum : set set set const ordsucc : set set const Empty : set const Inj1 : set set axiom Inj1_setsum_1L: !x:set.setsum (ordsucc Empty) x = Inj1 x axiom func_ext: !f:set set.!f2:set set.(!x:set.f x = f2 x) -> f = f2 claim Inj1 = setsum (ordsucc Empty)