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<b>let </b><font color="Maroon">Y</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">z</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">PA</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>, <font color="Maroon">PB</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/>





<b>assume </b><a NAME="E1:1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">PA</font> <a href="partit1.html#NR1" target="_self">'&lt;'</a> <font color="Maroon">PB</font>
 ;<br/>

<a NAME="E2:1"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">PA</font> &amp;  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">PA</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PA</font> )
 
<b>by </b><i><a class="ref" href="t_1topsp.html#D1">T_1TOPSP:def 1</a></i>;<br/>
<a NAME="E3:1"/>
 ex <font color="Olive">b</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PB</font> &amp;  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">PA</font> <a href="tarski.html#R1">c=</a> <font color="Olive">b</font> )
 
<b>by </b><i>, <a class="ref" href="setfam_1.html#D2">SETFAM_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:1"/>
 <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">PA</font> <a href="tarski.html#R1">c=</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">PB</font>
 <b>by </b><i>, <a class="ref" href="t_1topsp.html#D1">T_1TOPSP:def 1</a></i>;<br/>


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