const In : set set prop term iIn = In infix iIn 2000 2000 const omega : set const nat_p : set prop axiom omega_nat_p: !x:set.x iIn omega -> nat_p x const add_SNo : set set set term + = add_SNo infix + 2281 2280 const mul_SNo : set set set term * = mul_SNo infix * 2291 2290 const eps_ : set set lemma !x:set.!y:set.x iIn omega -> y iIn omega -> x + y iIn omega -> nat_p (x + y) -> eps_ x * eps_ y = eps_ (x + y) var x:set var y:set hyp x iIn omega hyp y iIn omega claim x + y iIn omega -> eps_ x * eps_ y = eps_ (x + y)