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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E24">Th32</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: MATRTOP1:32</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">m</font>, <font color="Olive" title="b3">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b4">A</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="b5">B</font> being   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Olive" title="b4">A</font>,<font color="Olive" title="b3">k</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  st ( <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies <font color="Olive" title="b2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) &amp; ( <font color="Olive" title="b2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies <font color="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) holds <br/><span class="p1">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Olive" title="b5">B</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Olive" title="b4">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">A</font> <a href="matrix_3.html#K5" title="MATRIX_3:func.5">*</a> <font color="Olive" title="b5">B</font></span>)</span></div></div>
