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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th16</font></span>: <a NAME="T16"><span class="comment"><font color="firebrick">:: MATRIXJ2:16</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="matrixj2.html#V2" title="MATRIXJ2:attr.2">nilpotent</a>  <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>  ex <font color="Olive" title="b4">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b2">V</font> st <br/> for <font color="Olive" title="b5">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b5">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="matrixj2.html#NK10" title="MATRIXJ2:NK.10">deg</a> <font color="Olive" title="b3">f</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Olive" title="b5">i</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">V</font></div></div>
