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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">LMTh44</font></span>: <a NAME="T23"><span class="comment"><font color="firebrick">:: ZMODUL07:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</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">W</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Olive" title="b1">R</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">A</font>, <font color="Olive" title="b6">B</font>, <font color="Olive" title="b7">X</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">V</font>  st <font color="Olive" title="b5">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <font color="Olive" title="b4">T</font></span>)</span> &amp; <font color="Olive" title="b7">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">B</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b5">A</font> holds <br/> <a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">T</font> <a href="ranknull.html#K2" title="RANKNULL:func.2">.:</a> <font color="Olive" title="b7">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">T</font> <a href="ranknull.html#K2" title="RANKNULL:func.2">.:</a> <font color="Olive" title="b6">B</font></span>)</span></div></div>
