Analytic discs and extension of CR functions

Let M be a manifold of X = C-n, A a small analytic disc attached to M, z(o) a point of partial derivativeA where A is tangent to M, z(1) another point of partial derivativeA where M extends to a germ of manifold M-1 with boun dary M. We prove that CR functions on M which extend to M-1 at z(1) also ex tend at z(o) to a new manifold M-2. The directions M-1 and M-2 point to, ar e related by a sort of connection associated to A which is dual to the conn ection obtained by attaching 'partial analytic lifts' of A to the co-normal bundle to M in X.