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<div><span class="kw">theorem </span><a NAME="T39"><span class="comment"><font color="firebrick">:: LMOD_6:39</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">K</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">V</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b3">W1</font>, <font color="Olive" title="b4">W2</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Olive" title="b2">V</font> holds <br/> ( <font color="Olive" title="b3">W1</font> <a href="lmod_6.html#R1" title="LMOD_6:pred.1">c=</a> <font color="Olive" title="b4">W2</font> iff  <a href="lmod_6.html#K2" title="LMOD_6:func.2">@</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Olive" title="b3">W1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lmod_6.html#K2" title="LMOD_6:func.2">@</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Olive" title="b4">W2</font></span>)</span> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="lmod_6.html#T38" target="_self" onmouseover="rs('lmod_6/T38')" onmouseout="rh()">Th38</a></span>;<br/></div></div>
