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<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>;<br/><b>let </b><font color="Maroon" title="c2">c1</font>, <font color="Maroon" title="c3">c2</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c1">L</font>;<br/><b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K3" title="WAYBEL10:func.3">ClOpers</a> <font color="Maroon" title="c1">L</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:27"/><i><font color="Green" title="E14">A1</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">c1</font> &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c2</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c6">x'</font> = <font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c7">y'</font> = <font color="Maroon" title="c5">y</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K7" title="YELLOW_1:func.7">MonMaps</a> <font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c1">L</font></span>)</span> <b>by </b><i><a class="ref" href="yellow_0.html#T59" title="YELLOW_0:th.59">YELLOW_0:59</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">x''</font> = <font color="Maroon" title="c6">x'</font>, <font color="Maroon" title="c9">y''</font> = <font color="Maroon" title="c7">y'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font></span>)</span> <b>by </b><i><a class="ref" href="yellow_0.html#T59" title="YELLOW_0:th.59">YELLOW_0:59</a></i>;<br/>
<a NAME="E4:27"/>
( <font color="Maroon" title="c8">x''</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">y''</font> iff <font color="Maroon" title="c6">x'</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">y'</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a>, <a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/>
<b>hence </b><a NAME="E5:27"/>
( <font color="Maroon" title="c4">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">y</font> iff <font color="Maroon" title="c2">c1</font> <a href="yellow_2.html#R1" title="YELLOW_2:pred.1">&lt;=</a> <font color="Maroon" title="c3">c2</font> )
 <b>by </b><i><a class="txt" href="waybel10.html#E1:27"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="waybel10.html#T12" target="_self" title="WAYBEL10:th.12">Th12</a>, <a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a>, <a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/>


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