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<div class="add">

<b>let </b><font color="Maroon" title="c1">R</font> be  <a href="group_1.html#V6" title="GROUP_1:attr.6">finite</a> <a href="vectsp_2.html#NM3" title="VECTSP_2:NM.3">Skew-Field</a>;<br/>

<a NAME="E1:32"/>
 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D21" title="VECTSP_1:def.21">VECTSP_1:def 21</a></i>;<br/>
<a NAME="E2:32"/><b>then </b><i><font color="Green" title="E27">A1</font></i>: 
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font></span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<b>by </b><i><a class="ref" href="card_2.html#T76" title="CARD_2:th.76">CARD_2:76</a></i>;<br/>
<a NAME="E3:32"/>
 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a>  <a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="ref" href="weddwitt.html#T19" target="_self" title="WEDDWITT:th.19">Th19</a></i>;<br/>
<a NAME="E4:32"/><b>then </b><i><font color="Green" title="E28">A2</font></i>: 
 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1" title="RLVECT_1:def.1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E5:32"/>
for <font color="Olive" title="b1">s</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> holds  <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">R</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">s</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>;<br/>

<font color="Maroon" title="c2">s</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">R</font></span>)</span> = 
<font color="Maroon" title="c2">s</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#D13" title="VECTSP_1:def.13">VECTSP_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c2">s</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></i>
;<br/>
<b>hence </b><a NAME="E2:32_1"/>
<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">R</font></span>)</span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E6:32"/><b>then </b>
 <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">R</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a>  <a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="ref" href="weddwitt.html#T18" target="_self" title="WEDDWITT:th.18">Th18</a></i>;<br/>
<a NAME="E7:32"/><b>then </b>
 <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1" title="RLVECT_1:def.1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E8:32"/><b>then </b>
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font></span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span>
 
<b>by </b><i><a class="txt" href="weddwitt.html#E4:32"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#T38" title="ZFMISC_1:th.38">ZFMISC_1:38</a></i>;<br/>
<a NAME="E9:32"/><b>then </b>
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span>
 
<b>by </b><i><a class="txt" href="weddwitt.html#E2:32"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="card_1.html#T80" title="CARD_1:th.80">CARD_1:80</a></i>;<br/>
<b>hence </b><a NAME="E10:32"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>


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