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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E50">Th55</font></span>: <a NAME="T55"><span class="comment"><font color="firebrick">:: MATRIX14:55</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">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">A</font> being   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of <font color="Olive" title="b1">n</font>,<font color="Olive" title="b2">K</font> holds <br/> (  ex <font color="Olive" title="b4">B1</font> being   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of <font color="Olive" title="b1">n</font>,<font color="Olive" title="b2">K</font> st <font color="Olive" title="b4">B1</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Olive" title="b3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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>) iff  ex <font color="Olive" title="b4">B2</font> being   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of <font color="Olive" title="b1">n</font>,<font color="Olive" title="b2">K</font> st <font color="Olive" title="b3">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Olive" title="b4">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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>) )</div></div>
