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<div><span class="kw">theorem </span><a NAME="T6"><span class="comment"><font color="firebrick">:: PARTIT_2:6</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Y</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">P</font>, <font color="Olive" title="b3">Q</font>, <font color="Olive" title="b4">R</font> being    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Olive" title="b1">Y</font>  st  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Olive" title="b4">R</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Olive" title="b2">P</font></span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Olive" title="b3">Q</font></span>)</span> holds <br/> for <font color="Olive" title="b5">x</font>, <font color="Olive" title="b6">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">Y</font> holds <br/> ( <font color="Olive" title="b5">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">EqClass</a> (<font color="Olive" title="b6">y</font>,<font color="Olive" title="b4">R</font>) iff  ex <font color="Olive" title="b7">z</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">Y</font> st <br/>( <font color="Olive" title="b5">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">EqClass</a> (<font color="Olive" title="b7">z</font>,<font color="Olive" title="b2">P</font>) &amp; <font color="Olive" title="b7">z</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">EqClass</a> (<font color="Olive" title="b6">y</font>,<font color="Olive" title="b3">Q</font>) ) )</div></div>
