feat(analysis/convex.cone): prove M. Riesz extension theorem, Hahn-Banach theorem (#2120)
* feat(analysis/convex.cone): prove M. Riesz extension theorem
WIP
* Complete the proof
TODO: move many facts to `linear_algebra/basic`,
fix possible build failures in other files
* Fix compile of `analysis/convex/cone`
* Cleanup, rewrite using `linear_pmap`s
* Deduce Hahn-Banach theorem from M. Riesz extension theorem
* Fix lint
* Apply suggestions from code review [skip_ci]
Co-Authored-By: sgouezel <sebastien.gouezel@univ-rennes1.fr>
* Expand comments, prove properties of `convex.to_cone`.
* Docstrings
* Apply suggestions from code review
Co-Authored-By: sgouezel <sebastien.gouezel@univ-rennes1.fr>
* Update src/analysis/convex/cone.lean
* Update src/linear_algebra/basic.lean
Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>