 Let formula_4 be a real analytic EDS.Assume that formula_5 is a connected, "formula_6"-dimensional, real analytic, regular integral manifold of "formula_1" with formula_8 (i.e., the tangent spaces formula_9 are "extendable" to higher dimensional integral elements).Moreover, assume there is a real analytic submanifold formula_10 of codimension formula_11 containing formula_12 and such that formula_13 has dimension formula_14 for all formula_15.