Allow empty Strongly Choquet spaces

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
 

theorems/T000172.md

@@ -1,9 +1,7 @@
 ---
 uid: T000172
 if:
-  and:
-  - P000122: true
-  - P000137: false
+  P000122: true
 then:
   P000206: true
 ---

theorems/T000317.md

@@ -1,9 +1,7 @@
 ---
 uid: T000317
 if:
-  and:
-  - P000051: true
-  - P000137: false
+  P000051: true
 then:
   P000206: true
 refs:

theorems/T000645.md

@@ -1,9 +1,7 @@
 ---
 uid: T000645
 if:
-  and:
-    - P000063: true
-    - P000137: false
+  P000063: true
 then:
   P000206: true
 refs:

theorems/T000647.md

@@ -1,9 +1,7 @@
 ---
 uid: T000647
 if:
-  and:
-  - P000094: true
-  - P000137: false
+  P000094: true
 then:
   P000206: true
 ---

theorems/T000680.md

@@ -4,8 +4,6 @@ if:
   and:
   - P000023: true
   - P000134: true
-  - P000137: false
-
 then:
   P000206: true
 ---