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<div><span class="kw">theorem </span><a NAME="T1"><span class="comment"><font color="firebrick">:: PRVECT_3:1</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">D</font>, <font color="Olive" title="b2">E</font>, <font color="Olive" title="b3">F</font>, <font color="Olive" title="b4">G</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>   ex <font color="Olive" title="b5">I</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b1">D</font>,<font color="Olive" title="b2">E</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b3">F</font>,<font color="Olive" title="b4">G</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b1">D</font>,<font color="Olive" title="b3">F</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b2">E</font>,<font color="Olive" title="b4">G</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> st <br/>( <font color="Olive" title="b5">I</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Olive" title="b5">I</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  &amp; (  for <font color="Olive" title="b6">d</font>, <font color="Olive" title="b7">e</font>, <font color="Olive" title="b8">f</font>, <font color="Olive" title="b9">g</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b6">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">D</font> &amp; <font color="Olive" title="b7">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">E</font> &amp; <font color="Olive" title="b8">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">F</font> &amp; <font color="Olive" title="b9">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">G</font> holds <br/><font color="Olive" title="b5">I</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b6">d</font>,<font color="Olive" title="b7">e</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b8">f</font>,<font color="Olive" title="b9">g</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b6">d</font>,<font color="Olive" title="b8">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b7">e</font>,<font color="Olive" title="b9">g</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> ) )</div></div>
