  We discuss the full nonlinear Kaluza-Klein (KK) reduction of the original
formulation of d=11 supergravity on $AdS_7\times S_4$ to gauged maximal ({\cal
N}=4) supergravity in 7 dimensions. We derive the full nonlinear embedding of
the d=7 fields in the d=11 fields (``the ansatz'') and check the consistency of
the ansatz by deriving the d=7 supersymmetry laws from the d=11 transformation
laws in the various sectors. The ansatz itself is nonpolynomial but the final
d=7 results are polynomial. The correct d=7 scalar potential is obtained. For
most of our results the explicit form of the matrix U connecting the d=7
gravitino to the Killing spinor is not needed, but we derive the equation which
U has to satisfy and present a solution. Requiring that the expression $\delta
F=d\delta A$ in d=11 can be written as $\delta d(fields in d=7)$, we find the
ansatz for the 4-form F. It satisfies the Bianchi identities. The corresponding
ansatz for A modifies the geometrical proposal by Freed et al. by including d=7
scalar fields. A first order formulation for the three index photon
$A_{\Lambda\Pi\Sigma}$ in d=11 is needed to obtain the d=7 supersymmetry laws
and the action for the nonabelian selfdual antisymmetric tensor field
$S_{\alpha\beta\gamma,A}$. Therefore selfduality in odd dimensions originates
from a first order formalism in higher dimensions.
