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| T_x (id)     =  id.
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| We may reformulate Proposition 2.2:
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| Proposition 2.3.  Let X, Y be manifolds of class C^p (p &gt;= 1)
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|                   modeled on Banach spaces.
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|                   Let f : X -&gt; Y be a C^p-morphism.
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|                   Let x be in X.
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|                   Then:
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|                   1.  f is an immersion at x if and only if
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|                       the map T_x f is injective and splits.
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|                   2.  f is a submersion at x if and only if
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|           