Autocomplete suggests lemma without namespace when scope is opened

Prerequisites

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Description

After writing open Nat, the LSP suggests div_eq_zero_iff instead of Nat.div_eq_zero_iff even though the lemma is protected.

Steps to Reproduce

1. Go to my Lean 4 Web example
2. In line 7, edit the div_eq_zero_iff identifier to provoke the autocomplete suggestions.
3. Get div_eq_zero_iff as a suggestion.
4. Select it, get "unknown identifier" error.

open Nat

-- The autocomplete suggests `div_eq_zero_iff` instead of `Nat.div_eq_zero_iff`,
-- even though it is protected
/-- error: Unknown identifier `div_eq_zero_iff` -/
#guard_msgs in
#check div_eq_zero_iff

Expected behavior:

Lean should suggest Nat.div_eq_zero_iff because the lemma is protected. In general, Lean should only suggest identifiers that won't lead to "unknown identifier" errors.

Actual behavior:

Lean strips the namespace, ignoring the protected modifier.

Versions

Lean 4.24.0-nightly-2025-08-20
Target: x86_64-unknown-linux-gnu

(Lean 4 Web)

Impact

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Start with the linked Lean 4 Web example and reproduce the completion after opening Nat, then inspect the LSP autocomplete behavior around the div_eq_zero_iff identifier. Done means the suggestion uses Nat.div_eq_zero_iff and selecting it no longer produces an unknown-identifier error.