Definition mod_aux_correct' : ltac:(auto_for_auto mod_aux_correct) := mod_aux_correct.
Hint Resolve mod_aux_correct' : eval.

Lemma mod_correct n m tn tm:
evaluates tn (value_of_N n) ->
evaluates tm (value_of_N m) ->
evaluates (modF (: tn, tm :)) (value_of_N (N.modulo n m)).