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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E3">Th3</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: CAT_3:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">A</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>   st <font color="Olive" title="b1">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">x2</font> holds <br/> for <font color="Olive" title="b4">y1</font>, <font color="Olive" title="b5">y2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b3">A</font> holds <br/> ( <span class="p1">(<span class="default">(<font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font>) <a href="funct_4.html#K7" title="FUNCT_4:func.7">--&gt;</a> (<font color="Olive" title="b4">y1</font>,<font color="Olive" title="b5">y2</font>)</span>)</span> <a href="funct_2.html#K10" title="FUNCT_2:func.10">/.</a> <font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">y1</font> &amp; <span class="p1">(<span class="default">(<font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font>) <a href="funct_4.html#K7" title="FUNCT_4:func.7">--&gt;</a> (<font color="Olive" title="b4">y1</font>,<font color="Olive" title="b5">y2</font>)</span>)</span> <a href="funct_2.html#K10" title="FUNCT_2:func.10">/.</a> <font color="Olive" title="b2">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">y2</font> )</div></div>
