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<div><span class="kw">theorem </span><a NAME="T20"><span class="comment"><font color="firebrick">:: ZMODUL04:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="vectsp_7.html#V3" title="VECTSP_7:attr.3">free</a>  <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a><br/>  for <font color="Olive" title="b2">I</font>, <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="b1">V</font>  st <font color="Olive" title="b2">I</font> is   <a href="zmodul03.html#NM1" title="ZMODUL03:NM.1">Basis</a> of <font color="Olive" title="b1">V</font> &amp; <font color="Olive" title="b2">I</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</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/> <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b3">A</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b2">I</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul04.html#T19" target="_self" onmouseover="rs('zmodul04/T19')" onmouseout="rh()">XXTh3</a>, <a class="ref" href="xboole_0.html#D8" onmouseover="rs('xboole_0/D8')" onmouseout="rh()">XBOOLE_0:def 8</a></span>;<br/></div></div>
