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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E46">Th42</font></span>: <a NAME="T42"><span class="comment"><font color="firebrick">:: MATRPROB:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">M</font>, <font color="Olive" title="b2">M1</font>, <font color="Olive" title="b3">M2</font> being   <a href="matrix_0.html#NM1" title="MATRIX_0:NM.1">Matrix</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Olive" title="b2">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">M2</font> holds <br/>( <font color="Olive" title="b1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">M1</font> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <font color="Olive" title="b3">M2</font> iff (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">M1</font> &amp;  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Olive" title="b1">M</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="b3">M2</font> &amp; (  for <font color="Olive" title="b4">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b4">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">M</font></span>)</span> holds <br/> <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Olive" title="b1">M</font>,<font color="Olive" title="b4">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="b2">M1</font>,<font color="Olive" title="b4">i</font>)</span>)</span> <a href="matrixr1.html#K12" title="MATRIXR1:func.12">*</a> <font color="Olive" title="b3">M2</font> ) ) )</div></div>
