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

(* Specifications: *)
Lemma succ_correct p: forall t,
evaluates t (value_of_pos p) ->
evaluates (succF (: t :)) (value_of_pos (Pos.succ p)).
Lemma add0_correct n m: forall tn tm,
evaluates tn (value_of_N n) ->
evaluates tm (value_of_N m) ->
evaluates (add0F (: tn, tm :)) (value_of_N (N.add n m)).