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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="waybel_0.html#V24">up-complete</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>



<b>assume </b><a NAME="E1:73"/><i><font color="Green">E32</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">S</font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">T</font> #)
 ;<br/>

<b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E2:73"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E3:73"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">D</font> being 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">S</font>  st  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">D</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Olive">D</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel11.html#D1">WAYBEL11:def 1</a><br/>

<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#D1">WAYBEL11:def 1</a><br/>

<b>assume </b><a NAME="E4:73"/><i><font color="Green">E37</font></i>: 
 <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">C</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">E</font> = <font color="Maroon">D</font> as  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">S</font> <b>by </b><i><a class="txt" href="yellow_9.html#E2:73"><i><font color="Green">E33</font></i></a>, <a class="ref" href="waybel_0.html#T3">WAYBEL_0:3</a></i>;<br/>
<a NAME="E6:73"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">E</font>,<font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="waybel_0.html#T75">WAYBEL_0:75</a></i>;<br/>
<a NAME="E7:73"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">E</font>
 
<b>by </b><i><a class="txt" href="yellow_9.html#E2:73"><i><font color="Green">E33</font></i></a>, <a class="ref" href="yellow_0.html#T26">YELLOW_0:26</a></i>;<br/>
<b>hence </b><a NAME="E8:73"/>
<font color="Maroon">D</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="txt" href="yellow_9.html#E3:73"><i><font color="Green">E35</font></i></a>, </i>;<br/>


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