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<div>:: <span class="kw">deftheorem </span>   defines <a href="topzari1.html#V1" title="TOPZARI1:attr.1">nilpotent</a> <a onclick="hs(this)" href="javascript:()">TOPZARI1:def 2 : <br/></a><span> for <font color="Olive" title="b1">A</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="group_1.html#V1" title="GROUP_1:attr.1">unital</a>   <a href="algstr_0.html#L5" title="ALGSTR_0:struct.5">multLoopStr_0</a> <br/>  for <font color="Olive" title="b2">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">A</font> holds <br/> ( <font color="Olive" title="b2">a</font> is  <a href="topzari1.html#V1" title="TOPZARI1:attr.1">nilpotent</a>  iff  ex <font color="Olive" title="b3">k</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Olive" title="b2">a</font> <a href="binom.html#K2" title="BINOM:func.2">|^</a> <font color="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">A</font> );<br/></span></div>
