feat(analysis/inner_product_space): proof of the Lax Milgram theorem (#11491)
My work on the Lax Milgram theorem, as suggested by @hrmacbeth. Done following the [slides from Peter Howard (Texas A&M University)](https://www.math.tamu.edu/~phoward/m612/s20/elliptic2.pdf).
Closes #10213.