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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid_7.html#K9" title="EUCLID_7:func.9">REAL-L</a> <font color="Maroon" title="c1">n</font></span>)</span>  st <font color="Olive" title="b1">B</font> is    <a href="rlvect_3.html#M1" title="RLVECT_3:mode.1">Basis</a> of  <a href="euclid_7.html#K9" title="EUCLID_7:func.9">REAL-L</a> <font color="Maroon" title="c1">n</font> holds <br/> <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font></span><br/><b>let </b><font color="Maroon" title="c2">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid_7.html#K9" title="EUCLID_7:func.9">REAL-L</a> <font color="Maroon" title="c1">n</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">B</font> is    <a href="rlvect_3.html#M1" title="RLVECT_3:mode.1">Basis</a> of  <a href="euclid_7.html#K9" title="EUCLID_7:func.9">REAL-L</a> <font color="Maroon" title="c1">n</font> implies  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> )</span><br/>



<b>assume </b><a NAME="E1:105"/><i><font color="Green" title="E56">A1</font></i>: 
<font color="Maroon" title="c2">B</font> is    <a href="rlvect_3.html#M1" title="RLVECT_3:mode.1">Basis</a> of  <a href="euclid_7.html#K9" title="EUCLID_7:func.9">REAL-L</a> <font color="Maroon" title="c1">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c3">Br</font> =  <a href="euclid_7.html#K8" title="EUCLID_7:func.8">RN_Base</a> <font color="Maroon" title="c1">n</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid_7.html#K9" title="EUCLID_7:func.9">REAL-L</a> <font color="Maroon" title="c1">n</font></span>)</span> ;<br/>
<a NAME="E3:105"/>
<font color="Maroon" title="c3">Br</font> is    <a href="rlvect_3.html#M1" title="RLVECT_3:mode.1">Basis</a> of  <a href="euclid_7.html#K9" title="EUCLID_7:func.9">REAL-L</a> <font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="ref" href="euclid_7.html#T48" target="_self" title="EUCLID_7:th.48">Th54</a></i>;<br/>
<a NAME="E4:105"/><b>then </b>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">Br</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="txt" href="#E1:105"><i><font color="Green" title="E56">A1</font></i></a>, <a class="ref" href="rlvect_5.html#T26" title="RLVECT_5:th.26">RLVECT_5:26</a></i>;<br/>
<b>hence </b><a NAME="E5:105"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="txt" href="euclid_7.html#E60"><i><font color="Green" title="E50">Lm3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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