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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K2">EqRelLatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>



<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> =  <a href="lattice3.html#NK17" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font> as   <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="msualg_7.html#T1">MSUALG_7:1</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:10"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:10"/><i><font color="Green">E6</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K2">EqRelLatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="txt" href="msualg_8.html#E4:10"><i><font color="Green">E6</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="msualg_7.html#T1">MSUALG_7:1</a></i>;<br/>
<a NAME="E7:10"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#R4">is_less_than</a>  <a href="lattice3.html#NK17" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="lattice3.html#D21">LATTICE3:def 21</a></i>;<br/>
<a NAME="E8:10"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#R3">[=</a>  <a href="lattice3.html#NK17" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="msualg_8.html#E4:10"><i><font color="Green">E6</font></i></a>, <a class="ref" href="lattice3.html#D17">LATTICE3:def 17</a></i>;<br/>
<a NAME="E9:10"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="msualg_8.html#T2" target="_self">Th2</a></i>;<br/>
<b>hence </b><a NAME="E10:10"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="lattice3.html#NK17" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="msualg_8.html#E4:10"><i><font color="Green">E6</font></i></a></i>;<br/>


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