fix(Tactic/Lift): preserve abbreviated target types

[sankalpsthakur]

lift n to MyNat using hn where MyNat is an abbrev could produce a proof term whose displayed/elaborated type unfolds the abbreviation to its underlying type, losing the connection to MyNat-specific declarations (e.g. a subsequent call to a MyNat-namespaced lemma would fail to resolve).

Wraps the synthesized proof term in an explicit show ∃ _ : $t, _ from … ascription using the originally-written target syntax t, so the abbreviation is preserved rather than unfolded.

Motivated by #15865.

Validation

• Built locally: lake build Mathlib.Tactic.Lift and lake build MathlibTest.Tactic.Lift — both succeed, including the new regression test (lifting to an abbrev-defined MyNat and calling a MyNat-namespaced lemma on the result).
• Scope note: lift is used in roughly 241 files across Mathlib. I verified the tactic's own implementation and its dedicated test suite build cleanly, but did not rebuild the full library to check every existing call site — the ascription should be semantically transparent (same term, explicit type), but I'm relying on CI for full-library confirmation rather than claiming that coverage myself.

Closes #15865

AI/LLM disclosure

AI coding tools were used to help draft this change and PR description. I reviewed the complete change, understand the reasoning, and verified the build locally before submitting.

[github-actions]

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[github-actions]

PR summary 49b60db482

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ MyNat
+ isTrue

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 49b60db).

• +0 new declarations
• −0 removed declarations

No declaration differences.

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 49b60db482
Reference commit 54df8a3f96

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).