End Fold2_With_Restriction.
Variable Tra :transpose2 f.

Lemma fold_right_add2 :
forall s' s i j x, NoDupA s -> NoDupA s' -> eqB i j -> ~ InA x s ->
equivlistA s' (x::s) -> eqB (fold_right f i s') (f x (fold_right f j s)).