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<span class="kw">set </span><font color="Maroon" title="c1">L</font> =  <a href="robbins1.html#K1" title="ROBBINS1:func.1">TrivComplLat</a> ;<br/>
<span class="kw">thus </span><a NAME="E1:16_1_1"/>
 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 <a href="robbins1.html#K1" title="ROBBINS1:func.1">TrivComplLat</a> holds  <font color="Olive" title="b1">x</font> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Olive" title="b1">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="lattices.html#D4" title="LATTICES:def.4">LATTICES:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="robbins1.html#K1" title="ROBBINS1:func.1">TrivComplLat</a>  is  <a href="lattices.html#V5" title="LATTICES:attr.5">join-associative</a>  &amp;  <a href="robbins1.html#K1" title="ROBBINS1:func.1">TrivComplLat</a>  is  <a href="robbins1.html#V5" title="ROBBINS1:attr.5">Robbins</a>  &amp;  <a href="robbins1.html#K1" title="ROBBINS1:func.1">TrivComplLat</a>  is  <a href="robbins1.html#V6" title="ROBBINS1:attr.6">Huntington</a>  &amp;  <a href="robbins1.html#K1" title="ROBBINS1:func.1">TrivComplLat</a>  is  <a href="robbins1.html#V7" title="ROBBINS1:attr.7">join-idempotent</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E2:16_1_1"/>
 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 <a href="robbins1.html#K1" title="ROBBINS1:func.1">TrivComplLat</a> holds  <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#NK4" title="ROBBINS1:NK.4">+</a> <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Olive" title="b3">z</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="robbins1.html#K1" title="ROBBINS1:func.1">TrivComplLat</a>  is  <a href="robbins1.html#V5" title="ROBBINS1:attr.5">Robbins</a>  &amp;  <a href="robbins1.html#K1" title="ROBBINS1:func.1">TrivComplLat</a>  is  <a href="robbins1.html#V6" title="ROBBINS1:attr.6">Huntington</a>  &amp;  <a href="robbins1.html#K1" title="ROBBINS1:func.1">TrivComplLat</a>  is  <a href="robbins1.html#V7" title="ROBBINS1:attr.7">join-idempotent</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E3:16_1_1"/>
 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 <a href="robbins1.html#K1" title="ROBBINS1:func.1">TrivComplLat</a> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">x</font> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b2">y</font> <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> <font color="Olive" title="b1">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">ROBBINS1:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="robbins1.html#K1" title="ROBBINS1:func.1">TrivComplLat</a>  is  <a href="robbins1.html#V6" title="ROBBINS1:attr.6">Huntington</a>  &amp;  <a href="robbins1.html#K1" title="ROBBINS1:func.1">TrivComplLat</a>  is  <a href="robbins1.html#V7" title="ROBBINS1:attr.7">join-idempotent</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E4:16_1_1"/>
 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 <a href="robbins1.html#K1" title="ROBBINS1:func.1">TrivComplLat</a> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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> <span class="p3">(<span class="default"><font color="Olive" title="b2">y</font> <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="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="robbins1.html#D6" target="_self" title="ROBBINS1:def.6">ROBBINS1:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="robbins1.html#K1" title="ROBBINS1:func.1">TrivComplLat</a>  is  <a href="robbins1.html#V7" title="ROBBINS1:attr.7">join-idempotent</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="robbins1.html#K1" title="ROBBINS1:func.1">TrivComplLat</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="robbins1.html#D7" target="_self" title="ROBBINS1:def.7">ROBBINS1:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font></span><br/>

<span class="kw">thus </span><a NAME="E5:16_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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