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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E6">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: LMOD_6:12</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">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">V</font><br/>  for <font color="Olive" title="b4">l</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Olive" title="b3">A</font>  st <font color="Olive" title="b3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b3">A</font> is  <a href="vectsp_4.html#V1" title="VECTSP_4:attr.1">linearly-closed</a>  holds <br/> <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Olive" title="b4">l</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">A</font></div></div>
