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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E36">HM1</font></span>: <a NAME="T42"><span class="comment"><font color="firebrick">:: ZMODUL06:42</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">X</font>, <font color="Olive" title="b3">Y</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">L</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b2">X</font>,<font color="Olive" title="b3">Y</font>  st <font color="Olive" title="b4">L</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  holds <br/> ex <font color="Olive" title="b5">K</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b3">Y</font>,<font color="Olive" title="b2">X</font> st <br/>( <font color="Olive" title="b5">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">L</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  &amp; <font color="Olive" title="b5">K</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  )</div></div>
