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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="group_1.html#V1">strict</a> <a href="group_1.html#NM1">Group</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:17"/><i><font color="Green">E18</font></i>: 
 <a href="group_1.html#K9">ord</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>and </b><br/><a NAME="E2:17"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E3:17"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#R1">in</a>  <a href="group_2.html#K5">(1).</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<a NAME="E1:17_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="gr_cy_1.html#E2:17"><i><font color="Green">E19</font></i></a></i>;<br/>
<a NAME="E2:17_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:17_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_2.html#K5">(1).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="group_2.html#D7">GROUP_2:def 7</a></i>;<br/>
<b>hence </b><a NAME="E4:17_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#R1">in</a>  <a href="group_2.html#K5">(1).</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:17"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_2.html#K5">(1).</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="group_2.html#T71">GROUP_2:71</a></i>;<br/>
<b>hence </b><a NAME="E5:17"/>
contradiction
 <b>by </b><i><a class="txt" href="gr_cy_1.html#E1:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="group_2.html#T81">GROUP_2:81</a></i>;<br/>


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