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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="orders_2.html#V3">transitive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V1">with_suprema</a> <a href="lattice3.html#V2">with_infima</a> <a href="yellow_0.html#V1">lower-bounded</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:33"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="yellow_5.html#R2" target="_self">meets</a> <font color="Maroon">c<sub>3</sub></font> <a href="yellow_5.html#K1" target="_self">\</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:33"/><i><font color="Green">E14</font></i>: 
not <font color="Maroon">c<sub>2</sub></font> <a href="yellow_5.html#R2" target="_self">meets</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="yellow_5.html#K1" target="_self">\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
<font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><a href="waybel_1.html#K7">'not'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7">'not'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7">'not'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="yellow_5.html#E2:33"><i><font color="Green">E14</font></i></a>, <a class="ref" href="yellow_5.html#D3" target="_self">Def3</a></i>
<br/>.= 
 <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="yellow_5.html#T28" target="_self">Th28</a></i>
;<br/>
<b>hence </b><a NAME="E4:33"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow_5.html#E1:33"><i><font color="Green">E13</font></i></a>, <a class="ref" href="yellow_5.html#D3" target="_self">Def3</a></i>;<br/>


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