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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">Th14</font></span>: <a NAME="T14"><span class="comment"><font color="firebrick">:: PARTIT_2:14</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">G</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="bvfunc_2.html#K1" title="BVFUNC_2:func.1">PARTITIONS</a> <font color="Olive" title="b1">Y</font></span>)</span>  st <font color="Olive" title="b2">G</font> is  <a href="bvfunc_2.html#V2" title="BVFUNC_2:attr.2">independent</a>  holds <br/> for <font color="Olive" title="b3">P</font>, <font color="Olive" title="b4">Q</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="bvfunc_2.html#K1" title="BVFUNC_2:func.1">PARTITIONS</a> <font color="Olive" title="b1">Y</font></span>)</span>  st <font color="Olive" title="b3">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">G</font> &amp; <font color="Olive" title="b4">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">G</font> holds <br/><span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <font color="Olive" title="b3">P</font></span>)</span></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> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <font color="Olive" title="b4">Q</font></span>)</span></span>)</span> <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> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <font color="Olive" title="b4">Q</font></span>)</span></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> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <font color="Olive" title="b3">P</font></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="partit_2.html#E14"><span class="lab"><font color="Green" title="E10">Lm1</font></span></a></span>;<br/></div></div>
