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<div><span class="kw">theorem </span><a NAME="T18"><span class="comment"><font color="firebrick">:: MOD_2:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">G</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Olive" title="b1">R</font> holds <br/> (  <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <span class="p1">(<span class="default"><a href="mod_2.html#K6" title="MOD_2:func.6">ID</a> <font color="Olive" title="b2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G</font> &amp;  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <span class="p1">(<span class="default"><a href="mod_2.html#K6" title="MOD_2:func.6">ID</a> <font color="Olive" title="b2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G</font> &amp; (  for <font color="Olive" title="b3">f</font> being   <a href="mod_2.html#V2" title="MOD_2:attr.2">strict</a>  <a href="mod_2.html#NM1" title="MOD_2:NM.1">LModMorphism</a> of <font color="Olive" title="b1">R</font>  st  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G</font> holds <br/><span class="p1">(<span class="default"><a href="mod_2.html#K6" title="MOD_2:func.6">ID</a> <font color="Olive" title="b2">G</font></span>)</span> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font> ) &amp; (  for <font color="Olive" title="b3">g</font> being   <a href="mod_2.html#V2" title="MOD_2:attr.2">strict</a>  <a href="mod_2.html#NM1" title="MOD_2:NM.1">LModMorphism</a> of <font color="Olive" title="b1">R</font>  st  <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Olive" title="b3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G</font> holds <br/><font color="Olive" title="b3">g</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <span class="p1">(<span class="default"><a href="mod_2.html#K6" title="MOD_2:func.6">ID</a> <font color="Olive" title="b2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">g</font> ) )</div></div>
