show/hide this revision's text 2 deleted 11 characters in body

There's a very terse proof of both the analytic inverse function thm and the analytic implicit function thm (where the second is rather "formally" deduced from the first) in the following book:

Fritzsche, Grauert, From Holomorphic Functions to Complex Manifolds

Chapter 7 "Holomorphic maps" (in which both theorems are proved) is freely available online.

show/hide this revision's text 1

There's a very terse proof of both the analytic inverse function thm and the analytic implicit function thm (where the second is rather "formally" deduced from the first) in the following book:

Fritzsche, Grauert, From Holomorphic Functions to Complex Manifolds

Chapter 7 "Holomorphic maps" (in which both theorems are proved) is freely available online.