diff --git a/doc/environments/groupthm/groupthm.dtx b/doc/environments/groupthm/groupthm.dtx
index 9476826..66314b5 100644
--- a/doc/environments/groupthm/groupthm.dtx
+++ b/doc/environments/groupthm/groupthm.dtx
@@ -714,8 +714,8 @@
 % {
 %   \groupthm_new_group:nn,
 %   \groupthm_renew_group:nn,
-%   \groupthm_provide_theorem_group:nn,
-%   \groupthm_declare_theorem_group:nn
+%   \groupthm_provide_group:nn,
+%   \groupthm_declare_group:nn
 % }
 %   \begin{syntax}
 %     \cs{groupthm_new_group:nn}\marg{keys}\marg{theorem group}
@@ -747,9 +747,9 @@
 % Non-keyval versions of
 % \cs{groupthm_new_group:nn},
 % \cs{groupthm_renew_group:nn},
-% \cs{groupthm_provide_theorem_group:nn}
+% \cs{groupthm_provide_group:nn}
 % and
-% \cs{groupthm_declare_theorem_group:nn}
+% \cs{groupthm_declare_group:nn}
 %
 % These take the individual values of the keyval keys directly, in the order
 % indicated by the syntax specification.
@@ -757,9 +757,9 @@
 % \end{function}
 % 
 %
-% \begin{function}{\groupthm_declare_theorem_group_rule:nnnn}
+% \begin{function}{\groupthm_declare_group_rule:nnnn}
 %    \begin{syntax}
-%       \cs{groupthm_declare_theorem_group_rule:nnnn}\marg{keyname}\marg{theorem group 1}
+%       \cs{groupthm_declare_group_rule:nnnn}\marg{keyname}\marg{theorem group 1}
 %       \marg{relation}\marg{theorem group 2}
 %    \end{syntax}
 %
@@ -1147,12 +1147,12 @@
 % 
 % 
 % 
-% \begin{variable}{\g_@@_defined_theorem_groups_clist}
+% \begin{variable}{\g_@@_defined_groups_clist}
 %		 
 %     This variable will hold a global list of declared theorem groups
 %
 %    \begin{macrocode}
-\clist_new:N \g_@@_defined_theorem_groups_clist
+\clist_new:N \g_@@_defined_groups_clist
 %    \end{macrocode}
 % \end{variable}
 %
@@ -1279,19 +1279,19 @@
 % Once there is such a proper mechanism, the author will likely update this to proper
 % string sorting.
 %
-% \begin{macro}{\@@_add_to_theorem_group_ordering:n}
+% \begin{macro}{\@@_add_to_group_ordering:n}
 %    \begin{syntax}
-%       \cs{@@_add_to_theorem_group_ordering:n}\marg{theorem group}
+%       \cs{@@_add_to_group_ordering:n}\marg{theorem group}
 %    \end{syntax}
 %		 
 %    Sets hook relations for this group and all already defined theorem groups.     
 %
 %    \begin{macrocode}
-\cs_new:Npn \@@_add_to_theorem_group_ordering:n #1
+\cs_new:Npn \@@_add_to_group_ordering:n #1
   {
     \@@_hook_gset_rule_foreach:nNnn
       { @@/groupsort }
-      \g_@@_defined_theorem_groups_clist
+      \g_@@_defined_groups_clist
       { before }
       { #1 }
   }
@@ -1300,19 +1300,19 @@
 %
 % 
 % 
-% \begin{macro}{\@@_remove_from_theorem_group_ordering:n}
+% \begin{macro}{\@@_remove_from_group_ordering:n}
 %    \begin{syntax}
-%       \cs{@@_remove_from_theorem_group_ordering:n}\marg{theorem group}
+%       \cs{@@_remove_from_group_ordering:n}\marg{theorem group}
 %    \end{syntax}
 %		 
 %    Removes all relations of this theorem group with the currently defined theorem groups.
 %
 %    \begin{macrocode}
-\cs_new:Npn \@@_remove_from_theorem_group_ordering:n #1
+\cs_new:Npn \@@_remove_from_group_ordering:n #1
   {
     \@@_hook_gset_rule_foreach:nNnn
       { @@/groupsort }
-      \g_@@_defined_theorem_groups_clist
+      \g_@@_defined_groups_clist
       { unrelated }
       { #1 }
   }
@@ -1343,7 +1343,7 @@
 % \end{macro}
 % 
 %
-% \begin{macro}{\@@_sort_theorem_group_names:}
+% \begin{macro}{\@@_sort_group_names:}
 %		 
 %     As explained briefly before, we first insert all theorems
 %     into the hook, clear the list, and then use the hook again.
@@ -1352,7 +1352,7 @@
 %     which is also assumed to hold only defined theorem group names.
 %
 %    \begin{macrocode}
-\cs_new:Npn \@@_sort_theorem_group_names:
+\cs_new:Npn \@@_sort_group_names:
   {
     \hook_gremove_code:nn { @@/groupsort  }{*}
     \clist_map_function:NN \l_@@_group_clist \@@_add_to_sort_hook:n
@@ -1413,13 +1413,13 @@
 % This ensures the ordering hacks explained before.
 %
 %    \begin{macrocode}
-    \@@_add_to_theorem_group_ordering:n { #1 }
+    \@@_add_to_group_ordering:n { #1 }
 %    \end{macrocode}
 %
 % Add defined group to corresponding list 
 %
 %    \begin{macrocode}
-    \clist_gput_left:Nn \g_@@_defined_theorem_groups_clist { #1 }
+    \clist_gput_left:Nn \g_@@_defined_groups_clist { #1 }
   }
 %    \end{macrocode}
 % \end{macro}
@@ -1457,7 +1457,7 @@
 % Remove theorem group from list of defined theorems
 %
 %    \begin{macrocode}
-    \clist_gremove_all:Nn  \g_@@_defined_theorem_groups_clist { #1 }
+    \clist_gremove_all:Nn  \g_@@_defined_groups_clist { #1 }
 %    \end{macrocode}
 %
 % Now, unset all relations with all defined theorem groups in the internal hooks.
@@ -1465,27 +1465,27 @@
 %    \begin{macrocode}
     \@@_hook_gset_rule_foreach:nNnn
       { ?? }
-      \g_@@_defined_theorem_groups_clist
+      \g_@@_defined_groups_clist
       { unrelated }
       { #1 }
     \@@_hook_gset_rule_foreach:nNnn
       { @@/prefix }
-      \g_@@_defined_theorem_groups_clist
+      \g_@@_defined_groups_clist
       { unrelated }
       { #1 }
     \@@_hook_gset_rule_foreach:nNnn
       { @@/suffix }
-      \g_@@_defined_theorem_groups_clist
+      \g_@@_defined_groups_clist
       { unrelated }
       { #1 }
     \@@_hook_gset_rule_foreach:nNnn
       { @@/mapname }
-      \g_@@_defined_theorem_groups_clist
+      \g_@@_defined_groups_clist
       { unrelated }
       { #1 }
     \@@_hook_gset_rule_foreach:nNnn
       { @@/thmtools }
-      \g_@@_defined_theorem_groups_clist
+      \g_@@_defined_groups_clist
       { unrelated }
       { #1 }
 %    \end{macrocode}
@@ -1493,7 +1493,7 @@
 % Also clear all sorting relations
 %
 %    \begin{macrocode}
-    \@@_remove_from_theorem_group_ordering:n { #1 }
+    \@@_remove_from_group_ordering:n { #1 }
   }
 %    \end{macrocode}
 % \end{macro}
@@ -1735,8 +1735,6 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \end{macro}
-%
 %
 %  Finally, we provide \LaTeX2e wrappers as document commands for these.
 %
@@ -1785,9 +1783,9 @@
 % We also provide the interface for declaring the precedence rules for theorem groups.
 %
 %
-% \begin{macro}{\groupthm_declare_theorem_group_rule:nnnn}
+% \begin{macro}{\groupthm_declare_group_rule:nnnn}
 %    \begin{syntax}
-%       \cs{groupthm_declare_theorem_group_rule:nnnn}\marg{keyname}\marg{theorem group 1}
+%       \cs{groupthm_declare_group_rule:nnnn}\marg{keyname}\marg{theorem group 1}
 %       \marg{relation}\marg{theorem group 2}
 %    \end{syntax}
 %		 
@@ -1797,7 +1795,7 @@
 % in case it is not the general hook \enquote{\texttt{??}}.
 %
 %    \begin{macrocode}
-\cs_new:Npn \groupthm_declare_theorem_group_rule:nnnn #1 #2 #3 #4
+\cs_new:Npn \groupthm_declare_group_rule:nnnn #1 #2 #3 #4
   {
     \str_set:Nx \l_tmpa_str { \tl_trim_spaces:n { #3 } }
     \str_if_eq:VnT \l_tmpa_str { higher }
@@ -1828,7 +1826,7 @@
 %    \begin{macrocode}
 \NewDocumentCommand { \DeclareTheoremGroupRule } { O{??} m m m }
   {
-    \groupthm_declare_theorem_group_rule:nnnn {#1} {#2} {#3} {#4}
+    \groupthm_declare_group_rule:nnnn {#1} {#2} {#3} {#4}
   }
 %    \end{macrocode}
 % \end{macro}
@@ -2456,7 +2454,7 @@
 % This sorting is necessary so that for each theorem family and set of groups,
 % the generated name will be unique:
 %    \begin{macrocode}
-        \@@_sort_theorem_group_names:
+        \@@_sort_group_names:
 %    \end{macrocode}
 % Now just declare the grouped theorem, passing the corresponding arguments and using
 % specified \texttt{\#6} as backend.
@@ -2996,7 +2994,7 @@
 % environment that has been generated by a \cs{NewGroupedTheoremFamily} command
 % or similar.
 %    \begin{macrocode}
-        \@@_sort_theorem_group_names:
+        \@@_sort_group_names:
         \cs_if_exist:cTF { __#1__groups_ \clist_use:Nn \l_@@_group_clist { _ } }
         {
           \begin { __#1__groups_ \clist_use:Nn \l_@@_group_clist { _ } }
@@ -3019,7 +3017,7 @@
 %    \end{macrocode}
 % End the corresponding environment.
 %    \begin{macrocode}
-        \@@_sort_theorem_group_names:
+        \@@_sort_group_names:
         \end { __#1__groups_ \clist_use:Nn \l_@@_group_clist { _ } }
       }
   }
diff --git a/doc/environments/groupthm/groupthm.sty b/doc/environments/groupthm/groupthm.sty
index a9d7c27..2bd03ad 100644
--- a/doc/environments/groupthm/groupthm.sty
+++ b/doc/environments/groupthm/groupthm.sty
@@ -84,7 +84,7 @@
 \clist_new:N \l__groupthm_mapname_clist
 \clist_new:N \l__groupthm_thmtools_clist
 \clist_new:N \l__groupthm_group_clist
-\clist_new:N \g__groupthm_defined_theorem_groups_clist
+\clist_new:N \g__groupthm_defined_groups_clist
 \bool_new:N  \l__groupthm_in_family_options_environment_bool
 \keys_define:nn { groupthm }
   {
@@ -130,19 +130,19 @@
     \clist_set_eq:NN \l__groupthm_mapname_clist  \l__groupthm_key_mapname_clist
     \clist_set_eq:NN \l__groupthm_thmtools_clist \l__groupthm_key_thmtools_clist
   }
-\cs_new:Npn \__groupthm_add_to_theorem_group_ordering:n #1
+\cs_new:Npn \__groupthm_add_to_group_ordering:n #1
   {
     \__groupthm_hook_gset_rule_foreach:nNnn
       { __groupthm/groupsort }
-      \g__groupthm_defined_theorem_groups_clist
+      \g__groupthm_defined_groups_clist
       { before }
       { #1 }
   }
-\cs_new:Npn \__groupthm_remove_from_theorem_group_ordering:n #1
+\cs_new:Npn \__groupthm_remove_from_group_ordering:n #1
   {
     \__groupthm_hook_gset_rule_foreach:nNnn
       { __groupthm/groupsort }
-      \g__groupthm_defined_theorem_groups_clist
+      \g__groupthm_defined_groups_clist
       { unrelated }
       { #1 }
   }
@@ -154,7 +154,7 @@
     \clist_put_left:Nn \l__groupthm_group_clist { #1 }
   }
 }
-\cs_new:Npn \__groupthm_sort_theorem_group_names:
+\cs_new:Npn \__groupthm_sort_group_names:
   {
     \hook_gremove_code:nn { __groupthm/groupsort  }{*}
     \clist_map_function:NN \l__groupthm_group_clist \__groupthm_add_to_sort_hook:n
@@ -182,8 +182,8 @@
           \clist_put_right:Nn \l__groupthm_thmtools_clist { #5 }
         }
     }
-    \__groupthm_add_to_theorem_group_ordering:n { #1 }
-    \clist_gput_left:Nn \g__groupthm_defined_theorem_groups_clist { #1 }
+    \__groupthm_add_to_group_ordering:n { #1 }
+    \clist_gput_left:Nn \g__groupthm_defined_groups_clist { #1 }
   }
 \cs_new:Npn \__groupthm_undefine_group:n #1
   {
@@ -193,33 +193,33 @@
     \hook_gremove_code:nn { __groupthm/suffix } { #1 }
     \hook_gremove_code:nn { __groupthm/mapname  } { #1 }
     \hook_gremove_code:nn { __groupthm/thmtools } { #1 }
-    \clist_gremove_all:Nn  \g__groupthm_defined_theorem_groups_clist { #1 }
+    \clist_gremove_all:Nn  \g__groupthm_defined_groups_clist { #1 }
     \__groupthm_hook_gset_rule_foreach:nNnn
       { ?? }
-      \g__groupthm_defined_theorem_groups_clist
+      \g__groupthm_defined_groups_clist
       { unrelated }
       { #1 }
     \__groupthm_hook_gset_rule_foreach:nNnn
       { __groupthm/prefix }
-      \g__groupthm_defined_theorem_groups_clist
+      \g__groupthm_defined_groups_clist
       { unrelated }
       { #1 }
     \__groupthm_hook_gset_rule_foreach:nNnn
       { __groupthm/suffix }
-      \g__groupthm_defined_theorem_groups_clist
+      \g__groupthm_defined_groups_clist
       { unrelated }
       { #1 }
     \__groupthm_hook_gset_rule_foreach:nNnn
       { __groupthm/mapname }
-      \g__groupthm_defined_theorem_groups_clist
+      \g__groupthm_defined_groups_clist
       { unrelated }
       { #1 }
     \__groupthm_hook_gset_rule_foreach:nNnn
       { __groupthm/thmtools }
-      \g__groupthm_defined_theorem_groups_clist
+      \g__groupthm_defined_groups_clist
       { unrelated }
       { #1 }
-    \__groupthm_remove_from_theorem_group_ordering:n { #1 }
+    \__groupthm_remove_from_group_ordering:n { #1 }
   }
 \cs_new:Npn \__groupthm_define:nnnNNNn #1 #2 #3 #4 #5 #6 #7
   {
@@ -343,7 +343,7 @@
   {
     \use:c { groupthm_ \declarator _group:nn } { ##1 } { ##2 }
   }
-\cs_new:Npn \groupthm_declare_theorem_group_rule:nnnn #1 #2 #3 #4
+\cs_new:Npn \groupthm_declare_group_rule:nnnn #1 #2 #3 #4
   {
     \str_set:Nx \l_tmpa_str { \tl_trim_spaces:n { #3 } }
     \str_if_eq:VnT \l_tmpa_str { higher }
@@ -365,7 +365,7 @@
 
 \NewDocumentCommand { \DeclareTheoremGroupRule } { O{??} m m m }
   {
-    \groupthm_declare_theorem_group_rule:nnnn {#1} {#2} {#3} {#4}
+    \groupthm_declare_group_rule:nnnn {#1} {#2} {#3} {#4}
   }
   % \subsection{Iterating over powersets}
 \clist_new:N  \l__powerset_copied_clist
@@ -631,7 +631,7 @@
       {
         \clist_set_eq:NN \l__groupthm_group_clist \l_tmpa_clist
         \clist_put_right:Nn \l__groupthm_group_clist { #5 }
-        \__groupthm_sort_theorem_group_names:
+        \__groupthm_sort_group_names:
         \use:c{groupthm_#6_grouped_theorem:xVnn}
           {__#1__groups_\clist_use:Nn \l__groupthm_group_clist {_}}
           \l__groupthm_group_clist
@@ -824,7 +824,7 @@
         #3
         \bool_set_false:N \l__groupthm_in_family_options_environment_bool
         \clist_put_right:Nn \l__groupthm_group_clist { #4 }
-        \__groupthm_sort_theorem_group_names:
+        \__groupthm_sort_group_names:
         \cs_if_exist:cTF { __#1__groups_ \clist_use:Nn \l__groupthm_group_clist { _ } }
         {
           \begin { __#1__groups_ \clist_use:Nn \l__groupthm_group_clist { _ } }
@@ -841,7 +841,7 @@
         #3
         \bool_set_false:N \l__groupthm_in_family_options_environment_bool
         \clist_put_right:Nn \l__groupthm_group_clist { #4 }
-        \__groupthm_sort_theorem_group_names:
+        \__groupthm_sort_group_names:
         \end { __#1__groups_ \clist_use:Nn \l__groupthm_group_clist { _ } }
       }
   }