feat: add normalize_instance% using core's normalizeInstance

[kim-em]

This PR adds a new normalize_instance% term elaborator that delegates to Lean core's
normalizeInstance (from leanprover/lean4#12897), and replaces ~53
fast_instance% call sites where the replacement is safe.

normalize_instance% is a thin wrapper (~15 lines) around Lean.Meta.normalizeInstance. Like
fast_instance%, it reduces instances to constructor applications and reuses canonical
sub-instances. Unlike fast_instance%, it works at instances transparency and delegates all
normalization logic to core.

The replaced sites cover:

• Equiv/type-alias transfers (WithAbs, WithConv, WithVal, WithLp, TransferInstance)
• Surjective constructors (Con, RingCon quotients, module congruences)
• DFunLike leaf instances (MultilinearMap, ContinuousMultilinearMap, AlternatingMap, Intertwining)
• Quotient instances (LinearAlgebra/Quotient/Defs)
• inferInstanceAs% sites (StandardPart, Presentation/Core)
• Miscellaneous (InfiniteAdeleRing, ZMod)

This PR doesn't attempt to replace all fast_instance%; it gets more complicated!

🤖 Prepared with Claude Code

[kim-em]

!radar

[github-actions]

PR summary 1fb91738ac

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ instance (v : AbsoluteValue R S) : Ring (WithAbs v) := normalize_instance% (equiv v).ring
+ instance : AddCommGroup (ContinuousMultilinearMap R M₁ M₂) := normalize_instance%
+ instance : AddCommGroup (M [⋀^ι]→L[R] N) := normalize_instance%
+ instance : AddCommGroup (MultilinearMap R M₁ M₂) := normalize_instance%
+ instance : Algebra P.Core R := normalize_instance% (inferInstanceAs <| Algebra P.core R)
+ instance : Algebra P.Core S := normalize_instance% (inferInstanceAs <| Algebra P.core S)
+ instance : CommRing (InfiniteAdeleRing K) := normalize_instance% Pi.commRing
+ instance : CommRing (WithAbs v) := normalize_instance% (equiv v).commRing
+ instance : CommRing (WithVal v) := normalize_instance% (equiv v).commRing
+ instance : CommRing P.Core := normalize_instance% (inferInstanceAs <| CommRing P.core)
+ instance : CommSemiring (WithAbs v) := normalize_instance% (equiv v).commSemiring
+ instance : Field (WithVal v) := normalize_instance% (equiv v).field
+ instance : Module R (M [⋀^ι]→L[A] N) := normalize_instance%
+ instance : Module R' (ContinuousMultilinearMap A M₁ M₂) := normalize_instance%
+ instance : Module S (MultilinearMap R M₁ M₂) := normalize_instance%
+ instance : MulAction R' (ContinuousMultilinearMap A M₁ M₂) := normalize_instance%
+ instance : MulAction R' (M [⋀^ι]→L[A] N) := normalize_instance%
+ instance [ContinuousAdd N] : DistribMulAction R (M [⋀^ι]→L[A] N) := normalize_instance%
- instance (v : AbsoluteValue R S) : Ring (WithAbs v) := fast_instance% (equiv v).ring
- instance : AddCommGroup (ContinuousMultilinearMap R M₁ M₂) := fast_instance%
- instance : AddCommGroup (M [⋀^ι]→L[R] N) := fast_instance%
- instance : AddCommGroup (MultilinearMap R M₁ M₂) := fast_instance%
- instance : Algebra P.Core R := fast_instance% (inferInstanceAs <| Algebra P.core R)
- instance : Algebra P.Core S := fast_instance% (inferInstanceAs <| Algebra P.core S)
- instance : CommRing (InfiniteAdeleRing K) := fast_instance% Pi.commRing
- instance : CommRing (WithAbs v) := fast_instance% (equiv v).commRing
- instance : CommRing (WithVal v) := fast_instance% (equiv v).commRing
- instance : CommRing P.Core := fast_instance% (inferInstanceAs <| CommRing P.core)
- instance : CommSemiring (WithAbs v) := fast_instance% (equiv v).commSemiring
- instance : Field (WithVal v) := fast_instance% (equiv v).field
- instance : Module R (M [⋀^ι]→L[A] N) := fast_instance%
- instance : Module R' (ContinuousMultilinearMap A M₁ M₂) := fast_instance%
- instance : Module S (MultilinearMap R M₁ M₂) := fast_instance%
- instance : MulAction R' (ContinuousMultilinearMap A M₁ M₂) := fast_instance%
- instance : MulAction R' (M [⋀^ι]→L[A] N) := fast_instance%
- instance [ContinuousAdd N] : DistribMulAction R (M [⋀^ι]→L[A] N) := fast_instance%
-+-+-+ addCommMonoid

You can run this locally as follows

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

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

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

---

No changes to technical debt.

You can run this locally as

./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).

[kim-em]

!radar

[kim-em]

!radar

[leanprover-radar]

Benchmark results for 41b9556 against 1fb9173 are in. There are no significant changes. @kim-em

• 🟥 build//instructions: +36.2G (+0.02%)

Small changes (1✅, 1🟥)

• 🟥 build/module/Mathlib.Combinatorics.Young.SemistandardTableau//instructions: +274.6M (+4.69%)
• ✅ build/module/Mathlib.Util.GetAllModules//instructions: -275.3M (-10.47%)

[JovanGerb]

I agree it would be nice to have the same backend implementation for both inferInstanceAs and fast_insance% (or its equivalent). The normalize instances function in core does still have some rought edges: I've seen it throw some kernel errors for no apparent reason. It would be interesting to see how much of the current fast_instance% can be replaces by normalize_instance% and how this affects performance.

(When we do merge this, the doc-string of normalize_instance% should be a standalone explanation, instead of comparing itself with fast_instance%)

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.