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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">C</font>, <font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>



<b>assume </b><a NAME="E1:8"/><i><font color="Green" title="E6">A1</font></i>: 
( <font color="Maroon" title="c2">C</font> is    <a href="taxonom1.html#M1" title="TAXONOM1:mode.1">Classification</a> of <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">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">C</font> )
 ;<br/>

<b>let </b><font color="Maroon" title="c4">a</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="E2:8"/><i><font color="Green" title="E7">A2</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">x</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c5">Y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:8"/><i><font color="Green" title="E8">A3</font></i>: 
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y</font> &amp; <font color="Maroon" title="c5">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> )
 <b>by </b><i><a class="txt" href="taxonom2.html#E1:8"><i><font color="Green" title="E6">A1</font></i></a>, <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">Y'</font> = <font color="Maroon" title="c5">Y</font> as    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="taxonom2.html#E1:8"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="taxonom2.html#E4:8"><i><font color="Green" title="E8">A3</font></i></a>, <a class="ref" href="partit1.html#D3" title="PARTIT1:def.3">PARTIT1:def 3</a></i>;<br/>
<a NAME="E6:8"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c6">Y'</font>
 
<b>by </b><i><a class="txt" href="taxonom2.html#E2:8"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="taxonom2.html#E4:8"><i><font color="Green" title="E8">A3</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/>
<b>hence </b><a NAME="E7:8"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 ;<br/>


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