From 7438d1e03910144e1776e18d6a7c7967d4b36edc Mon Sep 17 00:00:00 2001
From: Patrick Rabau <70125716+prabau@users.noreply.github.com>
Date: Tue, 13 Jan 2026 23:54:03 -0500
Subject: [PATCH 1/2] T806 equivalent rephrasing

---
 theorems/T000439.md | 6 +++++-
 theorems/T000806.md | 2 +-
 2 files changed, 6 insertions(+), 2 deletions(-)

diff --git a/theorems/T000439.md b/theorems/T000439.md
index 2c530bb2de..49d4f3b226 100644
--- a/theorems/T000439.md
+++ b/theorems/T000439.md
@@ -11,4 +11,8 @@ refs:
     name: Do compactness and sequential compactness coincide in countable spaces?
 ---
 
-Shown in {{mathse:4851117}}
+Shown in {{mathse:4851117}}.
+
+----
+*Note*: This theorem is an ingredient in the proof of the stronger result {T806};
+it is retained here for that reason.
diff --git a/theorems/T000806.md b/theorems/T000806.md
index 76d706f00d..96277a77f5 100644
--- a/theorems/T000806.md
+++ b/theorems/T000806.md
@@ -2,7 +2,7 @@
 uid: T000806
 if:
   and:
-  - P000019: true
+  - P000016: true
   - P000131: true
 then:
   P000020: true

From 4f16f597770f813b7d95a077e1c803f68440bb49 Mon Sep 17 00:00:00 2001
From: Patrick Rabau <70125716+prabau@users.noreply.github.com>
Date: Wed, 14 Jan 2026 16:18:19 -0500
Subject: [PATCH 2/2] T439 cleanup

---
 theorems/T000439.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/theorems/T000439.md b/theorems/T000439.md
index 49d4f3b226..9e0848481d 100644
--- a/theorems/T000439.md
+++ b/theorems/T000439.md
@@ -14,5 +14,4 @@ refs:
 Shown in {{mathse:4851117}}.
 
 ----
-*Note*: This theorem is an ingredient in the proof of the stronger result {T806};
-it is retained here for that reason.
+*Note*: This theorem is an ingredient in the proof of the stronger result {T806}.