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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E39">Th40</font></span>: <a NAME="T40"><span class="comment"><font color="firebrick">:: RANKNULL:40</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">V</font>, <font color="Olive" title="b3">W</font> being   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Olive" title="b1">F</font><br/>  for <font color="Olive" title="b4">T</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b2">V</font>,<font color="Olive" title="b3">W</font><br/>  for <font color="Olive" title="b5">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">V</font><br/>  for <font color="Olive" title="b6">B</font> being   <a href="vectsp_7.html#NM1" title="VECTSP_7:NM.1">Basis</a> of <font color="Olive" title="b2">V</font><br/>  for <font color="Olive" title="b7">l</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Olive" title="b6">B</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Olive" title="b5">A</font>  st <font color="Olive" title="b5">A</font> is   <a href="vectsp_7.html#NM1" title="VECTSP_7:NM.1">Basis</a> of <span class="p1">(<span class="default"><a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <font color="Olive" title="b4">T</font></span>)</span> &amp; <font color="Olive" title="b5">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b6">B</font> holds <br/><font color="Olive" title="b4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Olive" title="b7">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">T</font> <a href="ranknull.html#K8" title="RANKNULL:func.8">@</a> <font color="Olive" title="b7">l</font></span>)</span></div></div>
