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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V3">transitive</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:1"/><i><font color="Green">E2</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> : ( <font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="waybel_3.html#V1">compact</a> ) </span>}</span> 
 <b>by </b><i><a class="ref" href="waybel_8.html#D2">WAYBEL_8:def 2</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:1_1"/><i><font color="Green">E3</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E5:1_1"/><i><font color="Green">E4</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E6:1_1"/><i><font color="Green">E5</font></i>: 
<font color="Maroon">c<sub>5</sub></font> is <a href="waybel_3.html#V1">compact</a>
 ;<br/><a NAME="E7:1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="waybel13.html#E1:1"><i><font color="Green">E2</font></i></a>, <a class="txt" href="waybel13.html#E5:1_1"><i><font color="Green">E4</font></i></a>, <a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/><b>hence </b><a NAME="E8:1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="waybel13.html#E4:1_1"><i><font color="Green">E3</font></i></a>, <a class="txt" href="waybel13.html#E6:1_1"><i><font color="Green">E5</font></i></a>, <a class="ref" href="waybel_8.html#T4">WAYBEL_8:4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:1"/>
 <a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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