diff --git a/properties/P000206.md b/properties/P000206.md
index a6a983257..b3afcfa70 100644
--- a/properties/P000206.md
+++ b/properties/P000206.md
@@ -4,6 +4,8 @@ name: Strongly Choquet
 refs:
   - wikipedia: Choquet_game
     name: Choquet game on Wikipedia
+  - wikipedia: Normal_play_convention
+    name: Normal play convention on Wikipedia
   - zb: "0819.04002"
     name: Classical Descriptive Set Theory (Kechris)
 ---
@@ -16,6 +18,10 @@ and Player 2 chooses some open neighborhood $V_n\subseteq U_n$ of $x_n$.
 
 Player 2 wins this game provided $\bigcap\{U_n:n<\omega\}\not=\emptyset$.
 
+Note: We consider the {P137} space to be {P206} in the sense that
+Player 1 cannot make a legal move to start the game, and therefore loses immediately according
+to the {{wikipedia:Normal_play_convention}} of combinatorial games.
+
 ----
 #### Meta-properties
 
diff --git a/theorems/T000172.md b/theorems/T000172.md
index 40b4ea8a6..4135bf365 100644
--- a/theorems/T000172.md
+++ b/theorems/T000172.md
@@ -1,9 +1,7 @@
 ---
 uid: T000172
 if:
-  and:
-  - P000122: true
-  - P000137: false
+  P000122: true
 then:
   P000206: true
 ---
diff --git a/theorems/T000290.md b/theorems/T000290.md
deleted file mode 100644
index d8247f9ee..000000000
--- a/theorems/T000290.md
+++ /dev/null
@@ -1,14 +0,0 @@
----
-uid: T000290
-if:
-  P000078: true
-then:
-  P000064: true
-refs:
-  - mathse: 1143211
-    name: Intersection of two open dense sets is dense
-  - wikipedia: Baire_space
-    name: Baire space on Wikipedia
----
-
-A finite space has only finitely many open sets, and the intersection of two open dense sets is an open dense set, as shown for example in {{mathse:1143211}}.
diff --git a/theorems/T000317.md b/theorems/T000317.md
index dae343a03..b0d3d8aa9 100644
--- a/theorems/T000317.md
+++ b/theorems/T000317.md
@@ -1,9 +1,7 @@
 ---
 uid: T000317
 if:
-  and:
-  - P000051: true
-  - P000137: false
+  P000051: true
 then:
   P000206: true
 refs:
diff --git a/theorems/T000645.md b/theorems/T000645.md
index 2b7bc8097..0362694f6 100644
--- a/theorems/T000645.md
+++ b/theorems/T000645.md
@@ -1,9 +1,7 @@
 ---
 uid: T000645
 if:
-  and:
-    - P000063: true
-    - P000137: false
+  P000063: true
 then:
   P000206: true
 refs:
diff --git a/theorems/T000646.md b/theorems/T000646.md
deleted file mode 100644
index 8e45bf85e..000000000
--- a/theorems/T000646.md
+++ /dev/null
@@ -1,9 +0,0 @@
----
-uid: T000646
-if:
-  P000206: true
-then:
-  P000137: false
----
-
-By definition.
diff --git a/theorems/T000647.md b/theorems/T000647.md
index 0186f7627..d455ca34e 100644
--- a/theorems/T000647.md
+++ b/theorems/T000647.md
@@ -1,9 +1,7 @@
 ---
 uid: T000647
 if:
-  and:
-  - P000094: true
-  - P000137: false
+  P000094: true
 then:
   P000206: true
 ---
diff --git a/theorems/T000680.md b/theorems/T000680.md
index 0b43a8ea2..46f0aff5e 100644
--- a/theorems/T000680.md
+++ b/theorems/T000680.md
@@ -4,8 +4,6 @@ if:
   and:
   - P000023: true
   - P000134: true
-  - P000137: false
-  
 then:
   P000206: true
 ---