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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">Th57</font></span>: <a NAME="T57"><span class="comment"><font color="firebrick">:: ZMODUL02:57</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">V</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Olive" title="b1">R</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>  st  not <font color="Olive" title="b1">R</font> is  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  &amp; <font color="Olive" title="b3">A</font> is  <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  holds <br/> not  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">V</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">A</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_7.html#T2" onmouseover="rs('vectsp_7/T2')" onmouseout="rh()">VECTSP_7:2</a></span>;<br/></div></div>
