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<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel11.html#D2" target="_self">WAYBEL11:def 2</a><br/>

<b>assume </b><a NAME="E1:19_1_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">D</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">S</font> <a href="subset_1.html#K3">`</a> 
 ;<br/>

<b>assume </b><a NAME="E2:19_1_1"/>
not  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">D</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> <a href="subset_1.html#K3">`</a> 
 ;<br/>

<a NAME="E3:19_1_1"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">D</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#T10">YELLOW_6:10</a></i>;<br/>
<b>then consider </b><font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E5:19_1_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font>
 <b>and </b><br/><a NAME="E6:19_1_1"/><i><font color="Green">E54</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font> &amp; <font color="Olive">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">y</font> holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 <b>by </b><i/>;<br/>
<a NAME="E7:19_1_1"/>
<font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 
;<br/>
<a NAME="E8:19_1_1"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E9:19_1_1"/><b>then </b>
<font color="Maroon">D</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">S</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E10:19_1_1"/><b>then </b>
<font color="Maroon">D</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>hence </b><a NAME="E11:19_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/>


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