fix triple backslashes. add ensure group exists macro

doc/environments/groupthm/groupthm.dtx

@@ -1382,13 +1382,13 @@
   {
 %    \end{macrocode}
 %
-% \begin{macro}{\@@_use_group_\meta{theorem group}:}
+% \begin{macro}{\@@_use_group__\meta{theorem group}:}
 %
 % This is the internal macro that will be called when retrieving contents of a group.
 % We define this here to store the properties of the group.
 %
 %    \begin{macrocode}
-  \cs_new:cpn { @@_use_group_#1: }
+  \cs_new:cpn { @@_use_group__#1: }
     {
       \hook_gput_code:nnn { @@/prefix } { #1 }
         {
@@ -1442,7 +1442,7 @@
 \cs_new:Npn \@@_undefine_group:n #1
   {
     \tl_log:n { Undefining ~ theorem ~ group ~ '#1' }
-    \cs_undefine:c { @@_use_group_#1:   }
+    \cs_undefine:c { @@_use_group__#1:   }
 %    \end{macrocode}
 % 
 % Remove properties from hooks
@@ -1661,7 +1661,7 @@
 \@@_define_multiple:nnnNNnn
   { new, renew, provide, declare }
   { theorem group }
-  { @@_use_group_##1: }
+  { @@_use_group__##1: }
   \@@_undefine_group:n
   \@@_define_group:nnnnn
   { groupthm_#1_group:nnnnn }
@@ -1893,6 +1893,26 @@
 % \subsection{Grouped Theorems} 
 % 
 %
+%
+% \begin{macro}{\@@_ensure_group_exists:n}
+%    \begin{syntax}
+%       \cs{@@_ensure_group_exists:n}\meta{theorem group}
+%    \end{syntax}
+%		 
+%    Checks if this group exists.
+%    If not, produces an error message.
+%
+%    \begin{macrocode}
+\cs_new:Npn \@@_ensure_group_exists:n #1
+  {
+    \cs_if_exist:cF { @@_use_group__#1: }
+    {
+      \msg_error:nnn { groupthm } { unknown ~ group } { #1 }
+    }
+  }
+%    \end{macrocode}
+% \end{macro}
+% 
 % \begin{macro}{\@@_use_group:n}
 %    \begin{syntax}
 %       \cs{@@_use_group:n}\mymeta{theorem group}
@@ -1905,10 +1925,8 @@
 %    \begin{macrocode}
 \cs_new:Npn \@@_use_group:n #1
   {
-    \cs_if_exist_use:cF { @@_use_group_#1: }
+    \@@_ensure_group_exists:n { #1 }
-    {
+    \use:c { @@_use_group__#1: }
-      \msg_error:nnn { groupthm } { unknown ~ group } { #1 }
-    }
   }
 %    \end{macrocode}
 % \end{macro} 

doc/environments/groupthm/groupthm.sty

@@ -163,7 +163,7 @@
   }
 \cs_new:Npn \__groupthm_define_group:nnnnn #1#2#3#4#5
   {
-  \cs_new:cpn { __groupthm_use_group_#1: }
+  \cs_new:cpn { __groupthm_use_group__#1: }
     {
       \hook_gput_code:nnn { __groupthm/prefix } { #1 }
         {
@@ -188,7 +188,7 @@
 \cs_new:Npn \__groupthm_undefine_group:n #1
   {
     \tl_log:n { Undefining ~ theorem ~ group ~ '#1' }
-    \cs_undefine:c { __groupthm_use_group_#1:   }
+    \cs_undefine:c { __groupthm_use_group__#1:   }
     \hook_gremove_code:nn { __groupthm/prefix  } { #1 }
     \hook_gremove_code:nn { __groupthm/suffix } { #1 }
     \hook_gremove_code:nn { __groupthm/mapname  } { #1 }
@@ -288,7 +288,7 @@
 \__groupthm_define_multiple:nnnNNnn
   { new, renew, provide, declare }
   { theorem group }
-  { __groupthm_use_group_##1: }
+  { __groupthm_use_group__##1: }
   \__groupthm_undefine_group:n
   \__groupthm_define_group:nnnnn
   { groupthm_#1_group:nnnnn }
@@ -402,13 +402,18 @@
     \__powerset_clist_foreach_aux:Nn #1 {#2}
     \clist_set_eq:NN #1 \l__powerset_copied_clist
   }
-\cs_new:Npn \__groupthm_use_group:n #1
+\cs_new:Npn \__groupthm_ensure_group_exists:n #1
   {
-    \cs_if_exist_use:cF { __groupthm_use_group_#1: }
+    \cs_if_exist:cF { __groupthm_use_group__#1: }
     {
       \msg_error:nnn { groupthm } { unknown ~ group } { #1 }
     }
   }
+\cs_new:Npn \__groupthm_use_group:n #1
+  {
+    \__groupthm_ensure_group_exists:n { #1 }
+    \use:c { __groupthm_use_group__#1: }
+  }
 \cs_new:Npn \__groupthm_use_function_on_name:n #1
   {
     \tl_set:Nx \l__groupthm_name_tl