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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="lattices.html#NM1">Lattice</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/>



<a NAME="E1:52"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>thus </b><a NAME="E2:52"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#NR8" target="_self">is_great_than</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span> implies <font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>2</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:52_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#NR8" target="_self">is_great_than</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span>
 ;<br/>

<a NAME="E2:52_1"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="lattice3.html#E1:52"><i><font color="Green">E28</font></i></a>, <a class="ref" href="lattice3.html#D17" target="_self">Def17</a></i>;<br/>
<b>hence </b><a NAME="E3:52_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="filter_0.html#T6">FILTER_0:6</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E3:52"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D17" target="_self">LATTICE3:def 17</a><br/>

<b>assume </b><a NAME="E4:52"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span>
 ;<br/>

<a NAME="E5:52"/><b>then </b>
( ( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> ) &amp; <font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="lattices.html#T22">LATTICES:22</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E6:52"/>
<font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#R1">[=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="lattice3.html#E3:52"><i><font color="Green">E29</font></i></a>, <a class="ref" href="lattices.html#T25">LATTICES:25</a></i>;<br/>


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