Visibility of section variables is not verified correctly

Prerequisites

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• Reduce the issue to a minimal, self-contained, reproducible test case.
  Avoid dependencies to Mathlib or Batteries.
• Test your test case against the latest nightly release, for example on
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Description

In some cases, a section variable can be used in a theorem even if its type is private. In some other cases, Lean correctly rejects this, but the error message is confusing.

Steps to Reproduce

Run this:

module
import Std.Data.HashMap

structure X

variable {m : Std.HashMap Nat Nat} {n : X}

/--
error: Unknown constant `Std.HashMap`

Note: A public declaration `Std.HashMap` exists but is imported privately; consider adding `public import Std.Data.HashMap.Basic`.
---
error: Unknown constant `Std.HashMap`

Note: A public declaration `Std.HashMap` exists but is imported privately; consider adding `public import Std.Data.HashMap.Basic`.
-/
#guard_msgs in
public theorem a : m = m := rfl

#guard_msgs in
public theorem b : n = n := rfl

Expected behavior:

Theorems a and b should fail because they are relying on section variables with types that are not publicly visible.

In theorem a, the error message should explain that there is a problem with a section variable.

Actual behavior:

Theorem a fails, but the error message appears at the two m's in m = m. This is confusing: The theorem's signature doesn't explicitly reference the unknown constant Std.HashMap. It would be much better if the error message said something like: "The section variable m's type Std.HashMap Nat Nat is not visible in the public scope for the following reason: Unknown constant Std.HashMap [...]"

Theorem b succeeds even though n is of type X, which is a private constant.

Versions

Lean 4.25.0-nightly-2025-10-12
Target: x86_64-unknown-linux-gnu

Impact

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Run the supplied minimal reproducer against the Lean nightly release and compare the behavior and diagnostics for the public theorems a and b. Trace the section-variable visibility checking involved in this example; done means both declarations reject non-public types and theorem a reports the section variable and underlying visibility reason clearly.