ss C^p.  The verification of this assertion, whose formal
| details we leave to the reader, depends on the following obvious fact.
|
| Lang, DARM, page 23.
|
| Lemma 2.1.  Let U_1, U_2, V_1, V_2 be open subsets of Banach spaces,
|
|             and g : U_1 x U_2 -&gt; V_1 x V_2 a C^p-morphism.
|
|             Let a_2 be in U_2 and b_2 be in V_2
|
|             and assume that g maps U_1 x a_2 into V_1 x b_2.
|
|             Then the induced map
|
|             g_1 : U_1 -&gt; V_1
|
|             is also a m