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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th13</font></span>: <a NAME="T13"><span class="comment"><font color="firebrick">:: MATRIXJ2:13</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">K</font> being    <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/>  for <font color="Olive" title="b2">V</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">ModuleStr</a> over <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">V</font>,<font color="Olive" title="b2">V</font> holds <br/> ( <font color="Olive" title="b3">f</font> is  <a href="matrixj2.html#V2" title="MATRIXJ2:attr.2">nilpotent</a>  iff  ex <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Olive" title="b3">f</font> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Olive" title="b4">n</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="grcat_1.html#K6" title="GRCAT_1:func.6">ZeroMap</a> (<font color="Olive" title="b2">V</font>,<font color="Olive" title="b2">V</font>) )</div></div>
