<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">X</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K2" title="MSUALG_5:func.2">EqRelLatt</a> <font color="Maroon" title="c1">Y</font></span>)</span>;<br/>



<b>reconsider </b><font color="Maroon" title="c3">X'</font> =  <a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Maroon" title="c2">X</font> as   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c1">Y</font> <b>by </b><i><a class="ref" href="msualg_7.html#T1" title="MSUALG_7:th.1">MSUALG_7:1</a></i>;<br/>
<b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:10"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c2">X</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c5">X1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:10"/><i><font color="Green" title="E6">A1</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X1</font> &amp; <font color="Maroon" title="c5">X1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">X1</font> = <font color="Maroon" title="c5">X1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K2" title="MSUALG_5:func.2">EqRelLatt</a> <font color="Maroon" title="c1">Y</font></span>)</span> <b>by </b><i><a class="txt" href="msualg_8.html#E4:10"><i><font color="Green" title="E6">A1</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">X2</font> = <font color="Maroon" title="c6">X1</font> as   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c1">Y</font> <b>by </b><i><a class="ref" href="msualg_7.html#T1" title="MSUALG_7:th.1">MSUALG_7:1</a></i>;<br/>
<a NAME="E7:10"/>
<font color="Maroon" title="c2">X</font> <a href="lattice3.html#R4" title="LATTICE3:pred.4">is_less_than</a>  <a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Maroon" title="c2">X</font>
 
<b>by </b><i><a class="ref" href="lattice3.html#D21" title="LATTICE3:def.21">LATTICE3:def 21</a></i>;<br/>
<a NAME="E8:10"/><b>then </b>
<font color="Maroon" title="c6">X1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Maroon" title="c2">X</font>
 
<b>by </b><i><a class="txt" href="msualg_8.html#E4:10"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="lattice3.html#D17" title="LATTICE3:def.17">LATTICE3:def 17</a></i>;<br/>
<a NAME="E9:10"/><b>then </b>
<font color="Maroon" title="c7">X2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X'</font>
 
<b>by </b><i><a class="ref" href="msualg_8.html#T2" target="_self" title="MSUALG_8:th.2">Th2</a></i>;<br/>
<b>hence </b><a NAME="E10:10"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Maroon" title="c2">X</font>
 <b>by </b><i><a class="txt" href="msualg_8.html#E4:10"><i><font color="Green" title="E6">A1</font></i></a></i>;<br/>


</div>
