feat(algebraic_geometry/prime_spectrum): prime spectrum of a ring is compact (#1987)
* wip
* wip
* wip
* wip
* WIP
* WIP
* Reset changes that belong to other PR
* Docstrings
* Add Heine--Borel to docstring
* Cantor's intersection theorem
* Cantor for sequences
* Revert "Reset changes that belong to other PR"
This reverts commit e6026b8819570ef6a763582a25d7ae5ad508134b.
* Move submodule lemmas to other file
* Fix build
* Update prime_spectrum.lean
* Docstring
* Update prime_spectrum.lean
* Slight improvement?
* Slightly improve structure of proof
* WIP
* Cleaning up proofs
* Final fixes
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