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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a>   <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a>   <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a>   <a href="robbins3.html#V10" title="ROBBINS3:attr.10">naturally_sup-generated</a>   <a href="robbins3.html#L4" title="ROBBINS3:struct.4">OrthoLattRelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">x</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Olive" title="b2">y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">y</font></span><br/>



<a NAME="E1:91"/>
<font color="Maroon" title="c2">x</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></span>;<br/>
<a NAME="E2:91"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A1</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">y</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#T22" target="_self" title="ROBBINS3:th.22">Th22</a></span>;<br/>
<a NAME="E3:91"/>
<font color="Maroon" title="c2">x</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></span>;<br/>
<a NAME="E4:91"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A2</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">y</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#T22" target="_self" title="ROBBINS3:th.22">Th22</a></span>;<br/>
<a NAME="E5:91"/>
<font color="Maroon" title="c2">x</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">y</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T23" title="LATTICES:th.23">LATTICES:23</a></span>;<br/>
<a NAME="E6:91"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A3</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#T22" target="_self" title="ROBBINS3:th.22">Th22</a></span>;<br/>
<a NAME="E7:91"/>
<font color="Maroon" title="c2">x</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">y</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T23" title="LATTICES:th.23">LATTICES:23</a></span>;<br/>
<a NAME="E8:91"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A4</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#T22" target="_self" title="ROBBINS3:th.22">Th22</a></span>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">y</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">y</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice3.html#T16" title="LATTICE3:th.16">LATTICE3:16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:91"><span class="lab"><font color="Green" title="E35">A3</font></span></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></span>
<br/>.= 
<font color="Maroon" title="c2">x</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:91"><span class="lab"><font color="Green" title="E36">A4</font></span></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></span>
;<br/>
<a NAME="E10:91"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">x</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></span>;<br/>
<a NAME="E11:91"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A5</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">y</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">x</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#T22" target="_self" title="ROBBINS3:th.22">Th22</a></span>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">y</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">y</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D7" title="LATTICES:def.7">LATTICES:def 7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:91"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="lattices.html#T21" title="LATTICES:th.21">LATTICES:21</a></span>
<br/>.= 
<font color="Maroon" title="c2">x</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:91"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="ref" href="lattices.html#T21" title="LATTICES:th.21">LATTICES:21</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E13:91"/>
<font color="Maroon" title="c2">x</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:91"><span class="lab"><font color="Green" title="E37">A5</font></span></a>, <a class="ref" href="lattices.html#T21" title="LATTICES:th.21">LATTICES:21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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