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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E25">Th59</font></span>: <a NAME="T59"><span class="comment"><font color="firebrick">:: MATRIX_4:59</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">K</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b3">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b4">A</font>, <font color="Olive" title="b5">B</font> being   <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <font color="Olive" title="b2">K</font>  st  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Olive" title="b4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Olive" title="b5">B</font> &amp;  ex <font color="Olive" title="b6">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">i</font>,<font color="Olive" title="b6">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <font color="Olive" title="b4">A</font> holds <br/> <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<span class="p1">(<span class="default"><font color="Olive" title="b4">A</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Olive" title="b5">B</font></span>)</span>,<font color="Olive" title="b1">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Olive" title="b4">A</font>,<font color="Olive" title="b1">i</font>)</span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Olive" title="b5">B</font>,<font color="Olive" title="b1">i</font>)</span>)</span></div></div>
