Hint Resolve N_larger_bound_mod : eval.

Lemma mul_mod_correct n n' m b: forall tn tn' tm tb,
m <> 0 ->
N_larger_bound n b ->
evaluates tn (value_of_N n) ->
evaluates tn' (value_of_N n') ->
evaluates tm (value_of_N m) ->
evaluates tb (value_of_pos b) ->
evaluates (mul_modF (: tn, tn', tm, tb:))
((n * n') mod m).