               1.  f is an immersion at x if and only if
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|                       there exists a chart (U, q) at x and (V, r) at f(x)
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|                       such that f'_V,U(qx) is injective and splits.
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|                   2.  f is a submersion at x if and only if
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|                       there exists a chart (U, q) at x and (V, r) at f(x)
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|                       such that f'_V,U(qx) is surjective and its kernel splits.
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| Proof.  This is an immediate consequence
|         of Corollaries 5.4 and 5