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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">P</font> be    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font>, <font color="Maroon" title="c5">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>





<b>assume </b><a NAME="E1:7"/><i><font color="Green" title="E5">A1</font></i>: 
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P</font> &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P</font> &amp; <font color="Maroon" title="c5">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">x</font> &amp; <font color="Maroon" title="c5">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">y</font> )
 ;<br/>

<b>consider </b><font color="Maroon" title="c6">EqR</font> being   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E3:7"/><i><font color="Green" title="E6">A2</font></i>: 
<font color="Maroon" title="c2">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K9" title="EQREL_1:func.9">Class</a> <font color="Maroon" title="c6">EqR</font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#T43" title="EQREL_1:th.43">EQREL_1:43</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">x'</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E5:7"/><i><font color="Green" title="E7">A3</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c6">EqR</font>,<font color="Maroon" title="c7">x'</font>
 <b>by </b><i><a class="txt" href="taxonom2.html#E1:7"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="taxonom2.html#E3:7"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="eqrel_1.html#T45" title="EQREL_1:th.45">EQREL_1:45</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">y'</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E7:7"/><i><font color="Green" title="E8">A4</font></i>: 
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c6">EqR</font>,<font color="Maroon" title="c8">y'</font>
 <b>by </b><i><a class="txt" href="taxonom2.html#E1:7"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="taxonom2.html#E3:7"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="eqrel_1.html#T45" title="EQREL_1:th.45">EQREL_1:45</a></i>;<br/>
<b>thus </b><a NAME="E8:7"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font>
 <b>by </b><i><a class="txt" href="taxonom2.html#E1:7"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="taxonom2.html#E5:7"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="taxonom2.html#E7:7"><i><font color="Green" title="E8">A4</font></i></a>, <a class="ref" href="taxonom2.html#T2" target="_self" title="TAXONOM2:th.2">Th2</a></i>;<br/>


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