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<b>let </b><font color="Maroon">N</font> be  <a href="orders_2.html#V3">transitive</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">N</font>, <font color="Maroon">J</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">N</font>;<br/>



<b>assume </b><a NAME="E1:34"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">A</font> <a href="yellow_4.html#R2">is_coarser_than</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">J</font>
 ;<br/>

<b>let </b><font color="Maroon">w</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:34"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">w</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">A</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">w1</font> = <font color="Maroon">w</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font> ;<br/>
<b>consider </b><font color="Maroon">t</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font><b> such that </b><br/><a NAME="E5:34"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">t</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">w1</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 <b>by </b><i>, <a class="ref" href="waybel_0.html#D16">WAYBEL_0:def 16</a></i>;<br/>
<b>consider </b><font color="Maroon">t1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font><b> such that </b><br/><a NAME="E7:34"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">t1</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">J</font> &amp; <font color="Maroon">t1</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">t</font> )
 <b>by </b><i>, , <a class="ref" href="yellow_4.html#D2">YELLOW_4:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon">t2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font><b> such that </b><br/><a NAME="E9:34"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">t2</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">t1</font> &amp; <font color="Maroon">t2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">J</font> )
 <b>by </b><i>, <a class="ref" href="waybel_0.html#D16">WAYBEL_0:def 16</a></i>;<br/>
<a NAME="E10:34"/>
<font color="Maroon">t2</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">t</font>
 
<b>by </b><i>, , <a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/>
<a NAME="E11:34"/><b>then </b>
<font color="Maroon">t2</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">w1</font>
 
<b>by </b><i>, <a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/>
<b>hence </b><a NAME="E12:34"/>
<font color="Maroon">w</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">J</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#D16">WAYBEL_0:def 16</a></i>;<br/>


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