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I am focused on Chapter 2: Differentiation ... ...

I need help with an aspect of the proof of Proposition 2.2.9 ... ...

Duistermaat and Kolk's Proposition 2.2.9 and its proof read as follows:

View attachment 7844

In the above text D&K state that Lemma 1.1.7 (iv) implies Proposition 2.2.9 ...

Can someone please indicate how/why ths is the case ...

Peter

===========================================================================================The above post mentions Lemma 1.1.7 ... so I am providing the text of the same ... as follows:

View attachment 7845

View attachment 7846