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<b>set </b><font color="Maroon">f</font> =  <a href="waybel_2.html#K5" target="_self">sup_op</a> <font color="Maroon">L</font>;<br/>
<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">L</font>,<font color="Maroon">L</font></span><a href="yellow_3.html#K3">:]</a></span>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">L</font>,<font color="Maroon">L</font></span><a href="yellow_3.html#K3">:]</a></span>; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_3.html#D5">ORDERS_3:def 5</a><br/>

<b>assume </b><a NAME="E1:51_1_1"/>
<font color="Maroon">x</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">y</font>
 ;<br/>

<a NAME="E2:51_1_1"/><b>then </b><i><font color="Green">E29</font></i>: 
( <font color="Maroon">x</font> <a href="yellow_3.html#K8">`1</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">y</font> <a href="yellow_3.html#K8">`1</a>  &amp; <font color="Maroon">x</font> <a href="yellow_3.html#K9">`2</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">y</font> <a href="yellow_3.html#K9">`2</a>  )
 
<b>by </b><i><a class="ref" href="yellow_3.html#T12">YELLOW_3:12</a></i>;<br/>
<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>

<b>assume </b><a NAME="E3:51_1_1"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="waybel_2.html#K5" target="_self">sup_op</a> <font color="Maroon">L</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="waybel_2.html#K5" target="_self">sup_op</a> <font color="Maroon">L</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> )
 ;<br/>

<a NAME="E4:51_1_1"/>
( <span class="p1">(<span class="default"><a href="waybel_2.html#K5" target="_self">sup_op</a> <font color="Maroon">L</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="yellow_3.html#K8">`1</a> </span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="yellow_3.html#K9">`2</a> </span>)</span> &amp; <span class="p1">(<span class="default"><a href="waybel_2.html#K5" target="_self">sup_op</a> <font color="Maroon">L</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="yellow_3.html#K8">`1</a> </span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="yellow_3.html#K9">`2</a> </span>)</span> )
 
<b>by </b><i><a class="txt" href="waybel_2.html#E3:51_1_1"><i><font color="Green">E32</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:51_1_1"/>
<font color="Maroon">a</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font>
 <b>by </b><i>, , <a class="ref" href="yellow_3.html#T3">YELLOW_3:3</a></i>;<br/>


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