const nat_primrec : set (set set set) set set const ordsucc : set set term add_nat = \x:set.nat_primrec x \y:set.ordsucc const nat_p : set prop axiom nat_primrec_S: !x:set.!g:set set set.!y:set.nat_p y -> nat_primrec x g (ordsucc y) = g y (nat_primrec x g y) claim !x:set.!y:set.nat_p y -> add_nat x (ordsucc y) = ordsucc (add_nat x y)