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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   <a href="vectsp_7.html#V3" title="VECTSP_7:attr.3">free</a>   <a href="zmodul03.html#V1" title="ZMODUL03:attr.1">finite-rank</a>  <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font> being   <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font> holds  <font color="Olive" title="b1">I</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">I</font> be   <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">I</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> </span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">IV</font> =  the   <a href="zmodul03.html#NM1" title="ZMODUL03:NM.1">Basis</a> of <font color="Maroon" title="c1">V</font>;<br/>
<a NAME="E1:8"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c2">I</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a>  the   <a href="zmodul03.html#NM1" title="ZMODUL03:NM.1">Basis</a> of <font color="Maroon" title="c1">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul04.html#T20" onmouseover="rs('zmodul04/T20')" onmouseout="rh()">ZMODUL04:20</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:8"/>
<font color="Maroon" title="c2">I</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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