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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E24">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: VECTSP11:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">K</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b3">V1</font> being   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Olive" title="b2">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="b3">V1</font>,<font color="Olive" title="b3">V1</font> holds   <a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">f</font> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Olive" title="b1">i</font></span>)</span> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of  <a href="vectsp11.html#K2" title="VECTSP11:func.2">UnionKers</a> <font color="Olive" title="b4">f</font></div></div>
