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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E14">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: LMOD_7:12</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">W</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Olive" title="b2">V</font><br/>  for <font color="Olive" title="b4">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">V</font> <a href="lmod_7.html#K7" title="LMOD_7:func.7">..</a> <font color="Olive" title="b3">W</font>  ex <font color="Olive" title="b5">a</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b2">V</font> st <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a</font> <a href="lmod_7.html#K8" title="LMOD_7:func.8">..</a> <font color="Olive" title="b3">W</font></div></div>
