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<div><span class="kw">theorem </span><a NAME="T12"><span class="comment"><font color="firebrick">:: VECTSP12:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">K</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">V</font>, <font color="Olive" title="b3">U</font> being   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b4">f</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">U</font>  ex <font color="Olive" title="b5">T</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> (<font color="Olive" title="b2">V</font>,<span class="p2">(<span class="default"><a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <font color="Olive" title="b4">f</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <font color="Olive" title="b4">f</font></span>)</span> st <br/>( <font color="Olive" title="b5">T</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="vectsp12.html#K2" title="VECTSP12:func.2">CQFunctional</a> <font color="Olive" title="b4">f</font> &amp; <font color="Olive" title="b5">T</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  )</div></div>
