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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">Th16</font></span>: <a NAME="T16"><span class="comment"><font color="firebrick">:: MATRIX_3:16</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</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#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b3">i</font>, <font color="Olive" title="b4">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="b3">i</font>,<font color="Olive" title="b4">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> <span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Olive" title="b2">K</font>,<font color="Olive" title="b1">n</font>)</span>)</span> holds <br/>( ( <font color="Olive" title="b3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">j</font> implies <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<span class="p2">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Olive" title="b2">K</font>,<font color="Olive" title="b1">n</font>)</span>)</span>,<font color="Olive" title="b4">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b2">K</font> ) &amp; ( <font color="Olive" title="b3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">j</font> implies <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<span class="p2">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Olive" title="b2">K</font>,<font color="Olive" title="b1">n</font>)</span>)</span>,<font color="Olive" title="b4">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">K</font> ) )</div></div>
