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<div>:: <span class="kw">deftheorem </span>   defines <a href="bcialg_2.html#V5" title="BCIALG_2:attr.5">nilpotent</a> <a onclick="hs(this)" href="javascript:()">BCIALG_2:def 6 : <br/></a><span> for <font color="Olive" title="b1">X</font> being   <a href="bcialg_1.html#NM1" title="BCIALG_1:NM.1">BCI-algebra</a><br/>  for <font color="Olive" title="b2">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive" title="b2">x</font> is  <a href="bcialg_2.html#V5" title="BCIALG_2:attr.5">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 (<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">X</font></span>)</span>,<font color="Olive" title="b2">x</font>) <a href="bcialg_2.html#K1" title="BCIALG_2:func.1">to_power</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">X</font> );<br/></span></div>
