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<div><span class="kw">theorem </span><a NAME="T59"><span class="comment"><font color="firebrick">:: DBLSEQ_3:59</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C</font>, <font color="Olive" title="b2">D</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="b3">F1</font> being  <a href="mesfunc5.html#V3" title="MESFUNC5:attr.3">V183</a>() <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">C</font>,<font color="Olive" title="b2">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a><br/>  for <font color="Olive" title="b4">F2</font> being  <a href="mesfunc5.html#V4" title="MESFUNC5:attr.4">V184</a>() <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">C</font>,<font color="Olive" title="b2">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a><br/>  for <font color="Olive" title="b5">c</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">C</font> holds <br/> (  <a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">F1</font> <a href="dblseq_3.html#K4" title="DBLSEQ_3:func.4">-</a> <font color="Olive" title="b4">F2</font></span>)</span>,<font color="Olive" title="b5">c</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<font color="Olive" title="b3">F1</font>,<font color="Olive" title="b5">c</font>)</span>)</span> <a href="dblseq_3.html#K4" title="DBLSEQ_3:func.4">-</a> <span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<font color="Olive" title="b4">F2</font>,<font color="Olive" title="b5">c</font>)</span>)</span> &amp;  <a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p1">(<span class="default"><font color="Olive" title="b4">F2</font> <a href="dblseq_3.html#K5" title="DBLSEQ_3:func.5">-</a> <font color="Olive" title="b3">F1</font></span>)</span>,<font color="Olive" title="b5">c</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<font color="Olive" title="b4">F2</font>,<font color="Olive" title="b5">c</font>)</span>)</span> <a href="dblseq_3.html#K5" title="DBLSEQ_3:func.5">-</a> <span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<font color="Olive" title="b3">F1</font>,<font color="Olive" title="b5">c</font>)</span>)</span> )</div></div>
