open nat

definition f (a : nat) : nat := a
definition g (a : nat) : nat := 0

example (a b : nat) :
@eq nat
(g (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f a))))))))))))))))))))))
(g (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f b))))))))))))))))))))))
:=
@eq.refl nat (g (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f a))))))))))))))))))))))