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<b>let </b><font color="Maroon">L</font> be  <a href="orders_2.html#V3">transitive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V2">with_infima</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">D1</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>, <font color="Maroon">D2</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/>



<a NAME="E1:73"/><i><font color="Green">E20</font></i>: 
 <a href="waybel_0.html#K3">downarrow</a> <span class="p1">(<span class="default"><font color="Maroon">D1</font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">D2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">s</font> where <font color="Olive">s</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> :  ex <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">s</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">z</font> &amp; <font color="Olive">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D1</font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">D2</font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="waybel_0.html#T14">WAYBEL_0:14</a></i>;<br/>
<a NAME="E2:73"/><i><font color="Green">E21</font></i>: 
 <a href="waybel_0.html#K3">downarrow</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel_0.html#K3">downarrow</a> <font color="Maroon">D1</font></span>)</span> <a href="yellow_4.html#K4" target="_self">"/\"</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K3">downarrow</a> <font color="Maroon">D2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">x</font> where <font color="Olive">x</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> :  ex <font color="Olive">t</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">x</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">t</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K3">downarrow</a> <font color="Maroon">D1</font></span>)</span> <a href="yellow_4.html#K4" target="_self">"/\"</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K3">downarrow</a> <font color="Maroon">D2</font></span>)</span> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="waybel_0.html#T14">WAYBEL_0:14</a></i>;<br/>
<a NAME="E3:73"/><i><font color="Green">E30</font></i>: 
 <a href="waybel_0.html#K3">downarrow</a> <font color="Maroon">D1</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">s1</font> where <font color="Olive">s1</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> :  ex <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">s1</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">z</font> &amp; <font color="Olive">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D1</font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="waybel_0.html#T14">WAYBEL_0:14</a></i>;<br/>
<a NAME="E4:73"/><i><font color="Green">E32</font></i>: 
 <a href="waybel_0.html#K3">downarrow</a> <font color="Maroon">D2</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">s2</font> where <font color="Olive">s2</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> :  ex <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">s2</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">z</font> &amp; <font color="Olive">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D2</font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="waybel_0.html#T14">WAYBEL_0:14</a></i>;<br/>
<b>let </b><font color="Maroon">y</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="E5:73"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K3">downarrow</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel_0.html#K3">downarrow</a> <font color="Maroon">D1</font></span>)</span> <a href="yellow_4.html#K4" target="_self">"/\"</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K3">downarrow</a> <font color="Maroon">D2</font></span>)</span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E7:73"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>and </b><br/><a NAME="E8:73"/><i><font color="Green">E47</font></i>: 
 ex <font color="Olive">t</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Maroon">x</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">t</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K3">downarrow</a> <font color="Maroon">D1</font></span>)</span> <a href="yellow_4.html#K4" target="_self">"/\"</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K3">downarrow</a> <font color="Maroon">D2</font></span>)</span> )
 <b>by </b><i><a class="ref" href="yellow_4.html#T2" target="_self">Th2</a></i>;<br/>
<b>consider </b><font color="Maroon">x1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E10:73"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">x</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">x1</font>
 <b>and </b><br/><a NAME="E11:73"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K3">downarrow</a> <font color="Maroon">D1</font></span>)</span> <a href="yellow_4.html#K4" target="_self">"/\"</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K3">downarrow</a> <font color="Maroon">D2</font></span>)</span>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E13:73"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">b</font>
 <b>and </b><br/><a NAME="E14:73"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K3">downarrow</a> <font color="Maroon">D1</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K3">downarrow</a> <font color="Maroon">D2</font> )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">A1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E16:73"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A1</font>
 <b>and </b><br/><a NAME="E17:73"/><i><font color="Green">E81</font></i>: 
 ex <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Maroon">A1</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">z</font> &amp; <font color="Olive">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D1</font> )
 <b>by </b><i>, <a class="txt" href="yellow_4.html#E3:73"><i><font color="Green">E30</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">B1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E19:73"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B1</font>
 <b>and </b><br/><a NAME="E20:73"/><i><font color="Green">E84</font></i>: 
 ex <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Maroon">B1</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">z</font> &amp; <font color="Olive">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D2</font> )
 <b>by </b><i>, <a class="txt" href="yellow_4.html#E3:73"><i><font color="Green">E30</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">a1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E22:73"/><i><font color="Green">E85</font></i>: 
( <font color="Maroon">A1</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">a1</font> &amp; <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D1</font> )
 <b>by </b><i><a class="txt" href="yellow_4.html#E4:73"><i><font color="Green">E32</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">b1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E24:73"/><i><font color="Green">E86</font></i>: 
( <font color="Maroon">B1</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b1</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D2</font> )
 <b>by </b><i/>;<br/>
<a NAME="E25:73"/>
<font color="Maroon">x1</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">a1</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">b1</font>
 
<b>by </b><i>, , , , , <a class="ref" href="yellow_3.html#T2">YELLOW_3:2</a></i>;<br/>
<a NAME="E26:73"/><b>then </b><i><font color="Green">E87</font></i>: 
<font color="Maroon">x</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">a1</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">b1</font>
 
<b>by </b><i><a class="ref" href="yellow_4.html#D2" target="_self">Def2</a>, <a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/>
<a NAME="E27:73"/>
<font color="Maroon">a1</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D1</font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">D2</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E28:73"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K3">downarrow</a> <span class="p1">(<span class="default"><font color="Maroon">D1</font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">D2</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow_4.html#E2:73"><i><font color="Green">E21</font></i></a>, <a class="ref" href="yellow_4.html#D1" target="_self">Def1</a>, </i>;<br/>


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