chore(RingTheory/IntegralClosure/Algebra/Basic): generalize isIntegral_natCast and isIntegral_intCast

[tb65536]

This PR generalizes isIntegral_natCast and isIntegral_intCast to be over an arbitrary base ring. I also renamed the IsAlgebraic lemmas to match.

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[github-actions]

PR summary 98e54ce359

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 (regex)

+ isAlgebraic_intCast
+ isAlgebraic_natCast
+ isAlgebraic_ratCast

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 98e54ce).

• +3 new declarations
• −0 removed declarations

+isAlgebraic_intCast
+isAlgebraic_natCast
+isAlgebraic_ratCast

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 98e54ce359
Reference commit 783ccda4ee

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).

[mathlib-auto-merge]

As this PR is labelled auto-merge-after-CI, we are now sending it to bors:

bors merge

[mathlib-bors]

Merge conflict.

Merge or rebase master into this PR and resolve the conflict, then someone with permission can run bors r+ or bors retry.