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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E4">LM04</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: PETRI_3:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">X</font>, <font color="Olive" title="b3">Y</font>, <font color="Olive" title="b4">Z</font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Olive" title="b1">I</font>  st <font color="Olive" title="b2">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b3">Y</font> <a href="pboole.html#K4" title="PBOOLE:func.4">(\)</a> <font color="Olive" title="b4">Z</font> &amp; (  for <font color="Olive" title="b5">i</font>, <font color="Olive" title="b6">j</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">I</font> &amp; <font color="Olive" title="b6">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">I</font> &amp; <font color="Olive" title="b5">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">j</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b3">Y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">Z</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) holds <br/> <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Olive" title="b2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Olive" title="b3">Y</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Olive" title="b4">Z</font></span>)</span></div></div>
