In Spivak's "Calculus on Manifolds", his proof is *almost* coordinate free. I think his proof could be altered (as well as preceding results that he uses) basically by using a different metric to produce bounds. I'm pretty sure this is doable, and I'm going to write it up (so no spoilers, please!). But I'd like to make sure it's correct, and I'd like to see different points of view, of course.


I'd like to know: Are there any texts that prove the Inverse Function Theorem as coordinate-freely as possible? 


As a side note: I am not trying to *avoid* coordinates per-se for my intentions. Rather, I am trying to find different points of view for various basic constructions.



Any reference including a coordinate free proof of the inverse function theorem?
A coordinate-free proof of the inverse function
theorem in the finite-dimensional case
is provided by Theorem 19.6 in "Topological Geometry"
by Ian R. Porteous.


In general, the cited book is an exposition
of multivariable calculus in a coordinate-free manner.


