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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E17">Th20</font></span>: <a NAME="T20"><span class="comment"><font color="firebrick">:: MATRTOP1:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">M</font> being   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of <font color="Olive" title="b1">n</font>,<font color="Olive" title="b2">m</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a><br/>  for <font color="Olive" title="b4">Bn</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b1">n</font> <a href="prvect_1.html#K6" title="PRVECT_1:func.6">-VectSp_over</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a><br/>  for <font color="Olive" title="b5">Bm</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b2">m</font> <a href="prvect_1.html#K6" title="PRVECT_1:func.6">-VectSp_over</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  st <font color="Olive" title="b4">Bn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix13.html#K11" title="MATRIX13:func.11">MX2FinS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>,<font color="Olive" title="b1">n</font>)</span>)</span> &amp; <font color="Olive" title="b5">Bm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix13.html#K11" title="MATRIX13:func.11">MX2FinS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>,<font color="Olive" title="b2">m</font>)</span>)</span> holds <br/> for <font color="Olive" title="b6">M1</font> being   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b4">Bn</font>, <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b5">Bm</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  st <font color="Olive" title="b6">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">M</font> holds <br/> <a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Olive" title="b3">M</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Olive" title="b6">M1</font>,<font color="Olive" title="b4">Bn</font>,<font color="Olive" title="b5">Bm</font>)</div></div>
