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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E43">Th43</font></span>: <a NAME="T43"><span class="comment"><font color="firebrick">:: RANKNULL:43</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">X</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">l</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Olive" title="b4">T</font> <a href="ranknull.html#K2" title="RANKNULL:func.2">.:</a> <font color="Olive" title="b5">X</font>  st <font color="Olive" title="b4">T</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b5">X</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  holds <br/><font color="Olive" title="b4">T</font> <a href="ranknull.html#K8" title="RANKNULL:func.8">@</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">T</font> <a href="ranknull.html#K9" title="RANKNULL:func.9">#</a> <font color="Olive" title="b6">l</font></span>)</span> <a href="vectsp_6.html#R1" title="VECTSP_6:pred.1">=</a> <font color="Olive" title="b6">l</font></div></div>
