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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="lattices.html#V10">Lattice-like</a> <a href="lattice3.html#V1">with_suprema</a> <a href="lattice3.html#V2">with_infima</a> <a href="robbins3.html#V10" target="_self">naturally_sup-generated</a>  <a href="robbins3.html#L4" target="_self">OrthoLattRelStr</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>



<a NAME="E1:91"/>
<font color="Maroon">x</font> <a href="robbins3.html#NK3" target="_self">"|^|"</a> <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/>
<a NAME="E2:91"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">x</font> <a href="robbins3.html#NK3" target="_self">"|^|"</a> <font color="Maroon">y</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">x</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:91"/>
<font color="Maroon">x</font> <a href="robbins3.html#NK3" target="_self">"|^|"</a> <font color="Maroon">y</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#T23">YELLOW_0:23</a></i>;<br/>
<a NAME="E4:91"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">x</font> <a href="robbins3.html#NK3" target="_self">"|^|"</a> <font color="Maroon">y</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">y</font>
 
<b>by </b><i/>;<br/>
<i><font color="Green">E26</font></i>: <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="robbins3.html#NK3" target="_self">"|^|"</a> <font color="Maroon">y</font></span>)</span> <a href="robbins3.html#K4" target="_self">|^|</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="robbins3.html#K4" target="_self">|^|</a> <font color="Maroon">y</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="robbins3.html#NK3" target="_self">"|^|"</a> <font color="Maroon">y</font></span>)</span> <a href="robbins3.html#K4" target="_self">|^|</a> <font color="Maroon">x</font></span>)</span> <a href="robbins3.html#K4" target="_self">|^|</a> <font color="Maroon">y</font>
<b>by </b><i><a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="robbins3.html#NK3" target="_self">"|^|"</a> <font color="Maroon">y</font></span>)</span> <a href="robbins3.html#K4" target="_self">|^|</a> <font color="Maroon">y</font>
<b>by </b><i><a class="txt" href="robbins3.html#E9:91"><i><font color="Green">E33</font></i></a>, <a class="ref" href="lattices.html#T21">LATTICES:21</a></i>
<br/>.= 
<font color="Maroon">x</font> <a href="robbins3.html#NK3" target="_self">"|^|"</a> <font color="Maroon">y</font>
<b>by </b><i>, <a class="ref" href="lattices.html#T21">LATTICES:21</a></i>
;<br/>
<a NAME="E6:91"/>
<font color="Maroon">x</font> <a href="robbins3.html#K4" target="_self">|^|</a> <font color="Maroon">y</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">y</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T23">LATTICES:23</a></i>;<br/>
<a NAME="E7:91"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">x</font> <a href="robbins3.html#K4" target="_self">|^|</a> <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 
<b>by </b><i/>;<br/>
<a NAME="E8:91"/>
<font color="Maroon">x</font> <a href="robbins3.html#K4" target="_self">|^|</a> <font color="Maroon">y</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T23">LATTICES:23</a></i>;<br/>
<a NAME="E9:91"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">x</font> <a href="robbins3.html#K4" target="_self">|^|</a> <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font>
 
<b>by </b><i/>;<br/>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="robbins3.html#K4" target="_self">|^|</a> <font color="Maroon">y</font></span>)</span> <a href="robbins3.html#NK3" target="_self">"|^|"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="robbins3.html#NK3" target="_self">"|^|"</a> <font color="Maroon">y</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="robbins3.html#K4" target="_self">|^|</a> <font color="Maroon">y</font></span>)</span> <a href="robbins3.html#NK3" target="_self">"|^|"</a> <font color="Maroon">x</font></span>)</span> <a href="robbins3.html#NK3" target="_self">"|^|"</a> <font color="Maroon">y</font>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="robbins3.html#K4" target="_self">|^|</a> <font color="Maroon">y</font></span>)</span> <a href="robbins3.html#NK3" target="_self">"|^|"</a> <font color="Maroon">y</font>
<b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>
<br/>.= 
<font color="Maroon">x</font> <a href="robbins3.html#K4" target="_self">|^|</a> <font color="Maroon">y</font>
<b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>
;<br/>
<a NAME="E11:91"/><b>then </b>
<font color="Maroon">x</font> <a href="robbins3.html#K4" target="_self">|^|</a> <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="robbins3.html#NK3" target="_self">"|^|"</a> <font color="Maroon">y</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/>
<a NAME="E12:91"/><b>then </b>
<font color="Maroon">x</font> <a href="robbins3.html#K4" target="_self">|^|</a> <font color="Maroon">y</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">x</font> <a href="robbins3.html#NK3" target="_self">"|^|"</a> <font color="Maroon">y</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E13:91"/>
<font color="Maroon">x</font> <a href="robbins3.html#NK3" target="_self">"|^|"</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="robbins3.html#K4" target="_self">|^|</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="lattices.html#T21">LATTICES:21</a></i>;<br/>


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