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<div><span class="kw">theorem </span><a NAME="T27"><span class="comment"><font color="firebrick">:: VECTSP11:27</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">K</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">V</font> being   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  <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="b3">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="b2">V</font>  ex <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st  <a href="vectsp11.html#K2" title="VECTSP11:func.2">UnionKers</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Olive" title="b4">n</font></span>)</span></div></div>
