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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E31">Th27</font></span>: <a NAME="T27"><span class="comment"><font color="firebrick">:: MESFUN12:27</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X1</font>, <font color="Olive" title="b2">X2</font>, <font color="Olive" title="b3">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="b4">f</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"><font color="Olive" title="b1">X1</font>,<font color="Olive" title="b2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Olive" title="b3">Y</font><br/>  for <font color="Olive" title="b5">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X1</font><br/>  for <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="b2">X2</font> holds <br/> (  <a href="mesfun12.html#K2" title="MESFUN12:func.2">ProjPMap1</a> (<font color="Olive" title="b4">f</font>,<font color="Olive" title="b5">x</font>) <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<font color="Olive" title="b4">f</font>,<font color="Olive" title="b5">x</font>) &amp;  <a href="mesfun12.html#K3" title="MESFUN12:func.3">ProjPMap2</a> (<font color="Olive" title="b4">f</font>,<font color="Olive" title="b6">y</font>) <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<font color="Olive" title="b4">f</font>,<font color="Olive" title="b6">y</font>) )</div></div>
