feat(FieldTheory/Minpoly): `minpoly K x` splits implies `minpoly K (x + algebraMap K L a)` splits

[jjdishere]

We show that minpoly K x splits implies minpoly K (x + algebraMap K L a) splits.

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• [x] depends on: #17080
• [x] depends on: #17092

[github-actions[bot]]

PR summary c4bc187c17

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

+ Splits.comp_X_add_C + Splits.comp_X_sub_C + dvd_comp_X_add_C_iff + dvd_comp_X_sub_C_iff + minpoly_add_algebraMap_splits + minpoly_algebraMap_add_splits + minpoly_sub_algebraMap_splits

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.

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• ~~leanprover-community/mathlib4#17080~~
• ~~leanprover-community/mathlib4#17092~~ By Dependent Issues (🤖). Happy coding!

[jjdishere]

For the natural lemma that is missing in this PR, which is minpoly_algebraMap_sub_splits, please see #17369 .

[jcommelin]

maintainer merge

[github-actions[bot]]

🚀 Pull request has been placed on the maintainer queue by jcommelin.

[mathlib-bors[bot]]

Pull request successfully merged into master.

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