feat(RingTheory/IntegralClosure/IsIntegralClosure/Basic): Add lemmas about MvPolynomial and Polynomial

[su00000]

This PR proves : If I is an ideal of the polynomial ring S[X] and contains a monic polynomial f, then S[X]/I is integral over S. If a ≠ 0, then the degree of X_i in a monomial (MvPolynomial.monomial s) a is equal to s i. These lemmas will be used to prove the Noether Normalization lemma later.

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[github-actions[bot]]

PR summary 7892b78e4a

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ Polynomial.Monic.quotient_isIntegral + Polynomial.Monic.quotient_isIntegralElem + degreeOf_monomial_eq

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

[mathlib-bors[bot]]

:v: su00000 can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[kim-em]

@su00000, could you address the remaining comments above, and then remove that awaiting-author label so this can have a final round of review? Thanks!

[riccardobrasca]

Thanks!

bors mereg

[riccardobrasca]

bors merge

[mathlib-bors[bot]]

Pull request successfully merged into master.

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