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<b>let </b><font color="Maroon" title="c1">Y</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">z</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>;<br/><b>let </b><font color="Maroon" title="c3">PA</font> be    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font>;<br/>





<a NAME="E1:2"/>
(  <a href="partit1.html#K6" title="PARTIT1:func.6">%O</a> <font color="Maroon" title="c1">Y</font> <a href="partit1.html#NR2" title="PARTIT1:NR.2">'&gt;'</a> <font color="Maroon" title="c3">PA</font> &amp; <font color="Maroon" title="c3">PA</font> <a href="partit1.html#NR2" title="PARTIT1:NR.2">'&gt;'</a>  <a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font> )
 
<b>by </b><i><a class="ref" href="partit1.html#T36" title="PARTIT1:th.36">PARTIT1:36</a></i>;<br/>
<b>hence </b><a NAME="E2:2"/>
(  <a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">EqClass</a> <font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">PA</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">EqClass</a> <font color="Maroon" title="c2">z</font>,<span class="p1">(<span class="default"><a href="partit1.html#K6" title="PARTIT1:func.6">%O</a> <font color="Maroon" title="c1">Y</font></span>)</span> &amp;  <a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">EqClass</a> <font color="Maroon" title="c2">z</font>,<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">EqClass</a> <font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">PA</font> )
 <b>by </b><i><a class="ref" href="bvfunc11.html#T1" target="_self" title="BVFUNC11:th.1">Th1</a></i>;<br/>


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