feat(FieldTheory/IntermediateField): adjoining a shifted or scaled generator

[xroblot]

Add two lemmas about simple intermediate field extensions:

• IntermediateField.adjoin_simple_add_algebraMap: F⟮x + algebraMap F E y⟯ = F⟮x⟯ for y in the base field F.
• IntermediateField.adjoin_simple_mul_algebraMap: F⟮x * algebraMap F E y⟯ = F⟮x⟯ for y a nonzero element of F.

Translating the generator by a base-field element, or scaling it by a nonzero base-field element, leaves the simple extension unchanged.

🤖 This PR was extracted from the SKW project by Claude.

[github-actions]

PR summary 24085d1a55

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ adjoin_simple_add_algebraMap
+ adjoin_simple_mul_algebraMap

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

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

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 24085d1).

• +2 new declarations
• −0 removed declarations

+IntermediateField.adjoin_simple_add_algebraMap
+IntermediateField.adjoin_simple_mul_algebraMap

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 24085d1a55
Reference commit 2800ac2bd3

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).