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<b>let </b><font color="Maroon">L1</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> , <font color="Maroon">L2</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>assume </b><b>that </b><br/><a NAME="E1:28"/><i><font color="Green">E30</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L1</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">L2</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L2</font> #)
 <b>and </b><br/><a NAME="E2:28"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> holds <br/> (  <a href="waybel_3.html#K1">waybelow</a> <font color="Olive">x</font> is <a href="waybel_0.html#V1">directed</a> &amp; not  <a href="waybel_3.html#K1">waybelow</a> <font color="Olive">x</font> is <a href="xboole_0.html#V1">empty</a> )
 <b>and </b><br/><a NAME="E3:28"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> holds  <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K1">waybelow</a> <font color="Olive">x</font></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_3.html#D5">WAYBEL_3:def 5</a><br/>

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_3.html#D5">WAYBEL_3:def 5</a><br/>

<b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> <b>by </b><i/>;<br/>
<a NAME="E5:28"/>
(  <a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">y</font> is <a href="waybel_0.html#V1">directed</a> &amp; not  <a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">y</font> is <a href="xboole_0.html#V1">empty</a> )
 
<b>by </b><i/>;<br/>
<a NAME="E6:28"/><b>then </b><i><font color="Green">E38</font></i>: 
(  <a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">x</font> &amp;  <a href="yellow_0.html#R1">ex_sup_of</a>  <a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">y</font>,<font color="Maroon">L1</font> )
 
<b>by </b><i>, <a class="ref" href="waybel_0.html#T75">WAYBEL_0:75</a>, <a class="ref" href="yellow12.html#T13">YELLOW12:13</a></i>;<br/>
<a NAME="E7:28"/><b>then </b>
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">y</font></span>)</span> &amp;  <a href="yellow_0.html#R1">ex_sup_of</a>  <a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">x</font>,<font color="Maroon">L2</font> )
 
<b>by </b><i>, , <a class="ref" href="yellow_0.html#T14">YELLOW_0:14</a></i>;<br/>
<b>hence </b><a NAME="E8:28"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">x</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="yellow_0.html#T26">YELLOW_0:26</a></i>;<br/>


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