const In : set set prop term iIn = In infix iIn 2000 2000 term Subq = \x:set.\y:set.!z:set.z iIn x -> z iIn y const Inj1 : set set axiom Inj1I2: !x:set.!y:set.y iIn x -> Inj1 y iIn Inj1 x const ordsucc : set set const nat_p : set prop var x:set var y:set var z:set hyp nat_p x hyp !w:set.w iIn x -> Inj1 w = ordsucc w hyp y iIn x hyp z iIn y claim z iIn x -> ordsucc z iIn Inj1 x