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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E44">Th45</font></span>: <a NAME="T45"><span class="comment"><font color="firebrick">:: MATRIX13:45</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">i0</font>, <font color="Olive" title="b3">j0</font>, <font color="Olive" title="b4">n0</font>, <font color="Olive" title="b5">m0</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b6">A</font> being   <a href="matrix_0.html#NM1" title="MATRIX_0:NM.1">Matrix</a> of <font color="Olive" title="b1">D</font>  st <font color="Olive" title="b2">i0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b3">j0</font> &amp; <font color="Olive" title="b4">n0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b5">m0</font> holds <br/> <a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> (<font color="Olive" title="b6">A</font>,<span class="p1"><a href="matrix13.html#K4" title="MATRIX13:func.4">{</a><span class="default"><font color="Olive" title="b2">i0</font>,<font color="Olive" title="b3">j0</font></span><a href="matrix13.html#K4" title="MATRIX13:func.4">}</a></span>,<span class="p1"><a href="matrix13.html#K4" title="MATRIX13:func.4">{</a><span class="default"><font color="Olive" title="b4">n0</font>,<font color="Olive" title="b5">m0</font></span><a href="matrix13.html#K4" title="MATRIX13:func.4">}</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<span class="p1">(<span class="default"><font color="Olive" title="b6">A</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Olive" title="b2">i0</font>,<font color="Olive" title="b4">n0</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b6">A</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Olive" title="b2">i0</font>,<font color="Olive" title="b5">m0</font>)</span>)</span>) <a href="matrix_0.html#K15" title="MATRIX_0:func.15">][</a> (<span class="p1">(<span class="default"><font color="Olive" title="b6">A</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Olive" title="b3">j0</font>,<font color="Olive" title="b4">n0</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b6">A</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Olive" title="b3">j0</font>,<font color="Olive" title="b5">m0</font>)</span>)</span>)</div></div>
