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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="robbins2.html#V1" title="ROBBINS2:attr.1">satisfying_DN_1</a>  <a href="robbins1.html#L2" title="ROBBINS1:struct.2">ComplLattStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Olive" title="b3">z</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Olive" title="b1">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span><br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">z</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c4">z</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span><br/>



<b>set </b><font color="Maroon" title="c5">X</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> ;<br/>
<b>set </b><font color="Maroon" title="c6">Z</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> ;<br/>
<b>set </b><font color="Maroon" title="c7">Y</font> = <font color="Maroon" title="c4">z</font>;<br/>
<a NAME="E1:14"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c4">z</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<b>by </b><i><a class="ref" href="robbins2.html#T9" target="_self" title="ROBBINS2:th.9">Th9</a></i>;<br/>
<b>hence </b><a NAME="E2:14"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c4">z</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="robbins2.html#T6" target="_self" title="ROBBINS2:th.6">Th6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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