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<b>let </b><font color="Maroon">L</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">c1</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L</font>,<font color="Maroon">L</font>, <font color="Maroon">c2</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L</font>,<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">(<span class="default"><a href="waybel10.html#K3" target="_self">ClOpers</a> <font color="Maroon">L</font></span>)</span>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K3" target="_self">ClOpers</a> <font color="Maroon">L</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:27"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c1</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c2</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font>, <font color="Maroon">y'</font> = <font color="Maroon">y</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K7">MonMaps</a> <font color="Maroon">L</font>,<font color="Maroon">L</font></span>)</span> <b>by </b><i><a class="ref" href="yellow_0.html#T59">YELLOW_0:59</a></i>;<br/>
<b>reconsider </b><font color="Maroon">x''</font> = <font color="Maroon">x'</font>, <font color="Maroon">y''</font> = <font color="Maroon">y'</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="yellow_1.html#K6">|^</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font></span>)</span> <b>by </b><i><a class="ref" href="yellow_0.html#T59">YELLOW_0:59</a></i>;<br/>
<a NAME="E4:27"/>
( <font color="Maroon">x''</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y''</font> iff <font color="Maroon">x'</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y'</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a>, <a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/>
<b>hence </b><a NAME="E5:27"/>
( <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> iff <font color="Maroon">c1</font> <a href="yellow_2.html#R1">&lt;=</a> <font color="Maroon">c2</font> )
 <b>by </b><i>, , <a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a>, <a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/>


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