Hint Resolve N_larger_bound_mod : eval.

Lemma exp_mod_correct x y m tx ty tm:
m <> 0 ->
evaluates tx (value_of_N x) ->
evaluates ty (value_of_N y) ->
evaluates tm (value_of_N m) ->
evaluates (exp_modF (: tx, ty, tm :))
( x ^ y mod m).