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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E61">Th62</font></span>: <a NAME="T62"><span class="comment"><font color="firebrick">:: MATRIX13:62</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">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="b2">A</font> being   <a href="matrix_0.html#NM1" title="MATRIX_0:NM.1">Matrix</a> of <font color="Olive" title="b1">D</font><br/>  for <font color="Olive" title="b3">P</font>, <font color="Olive" title="b4">Q</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">without_zero</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  st <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b3">P</font>,<font color="Olive" title="b4">Q</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <font color="Olive" title="b2">A</font> &amp; (  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b4">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b3">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) holds <br/> <a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">P</font>,<font color="Olive" title="b4">Q</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<span class="p2">(<span class="default"><font color="Olive" title="b2">A</font> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span>,<font color="Olive" title="b4">Q</font>,<font color="Olive" title="b3">P</font>)</span>)</span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a> </div></div>
