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<div><span class="kw">theorem </span><a NAME="T23"><span class="comment"><font color="firebrick">:: GRCAT_1:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="vectsp_1.html#NM1" title="VECTSP_1:NM.1">AddGroup</a> holds <br/> (  <a href="grcat_1.html#K7" title="GRCAT_1:func.7">dom</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K11" title="GRCAT_1:func.11">ID</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G</font> &amp;  <a href="grcat_1.html#K8" title="GRCAT_1:func.8">cod</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K11" title="GRCAT_1:func.11">ID</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G</font> &amp; (  for <font color="Olive" title="b2">f</font> being   <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">strict</a>  <a href="grcat_1.html#NM1" title="GRCAT_1:NM.1">GroupMorphism</a>  st  <a href="grcat_1.html#K8" title="GRCAT_1:func.8">cod</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G</font> holds <br/><span class="p1">(<span class="default"><a href="grcat_1.html#K11" title="GRCAT_1:func.11">ID</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="grcat_1.html#K13" title="GRCAT_1:func.13">*</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> ) &amp; (  for <font color="Olive" title="b2">g</font> being   <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">strict</a>  <a href="grcat_1.html#NM1" title="GRCAT_1:NM.1">GroupMorphism</a>  st  <a href="grcat_1.html#K7" title="GRCAT_1:func.7">dom</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G</font> holds <br/><font color="Olive" title="b2">g</font> <a href="grcat_1.html#K13" title="GRCAT_1:func.13">*</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K11" title="GRCAT_1:func.11">ID</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font> ) )</div></div>
