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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E23">Th44</font></span>: <a NAME="T24"><span class="comment"><font color="firebrick">:: ZMODUL07:24</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font>, <font color="Olive" title="b2">W</font> being   <a href="vectsp_7.html#V3" title="VECTSP_7:attr.3">free</a>   <a href="zmodul03.html#V1" title="ZMODUL03:attr.1">finite-rank</a>  <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a><br/>  for <font color="Olive" title="b3">T</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">W</font> holds   <a href="zmodul03.html#K1" title="ZMODUL03:func.1">rank</a> <font color="Olive" title="b1">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zmodul07.html#K4" title="ZMODUL07:func.4">rank</a> <font color="Olive" title="b3">T</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="zmodul07.html#K5" title="ZMODUL07:func.5">nullity</a> <font color="Olive" title="b3">T</font></span>)</span></div></div>
