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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E99">Th122</font></span>: <a NAME="T116"><span class="comment"><font color="firebrick">:: GROUP_24:116</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>   <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b2">k</font> &amp; <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2 holds <br/> for <font color="Olive" title="b3">g1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="gr_cy_1.html#K4" title="GR_CY_1:func.4">INT.Group</a> <font color="Olive" title="b1">n</font></span>)</span>  st <font color="Olive" title="b3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/> for <font color="Olive" title="b4">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="group_24.html#K6" title="GROUP_24:func.6">Dihedral_group</a> <font color="Olive" title="b1">n</font></span>)</span>  st <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="group_7.html#K5" title="GROUP_7:func.5">&lt;*</a><span class="default"><font color="Olive" title="b3">g1</font>,<span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p3">(<span class="default"><a href="gr_cy_1.html#K4" title="GR_CY_1:func.4">INT.Group</a> 2</span>)</span></span>)</span></span><a href="group_7.html#K5" title="GROUP_7:func.5">*&gt;</a></span> holds <br/> for <font color="Olive" title="b5">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="group_24.html#K6" title="GROUP_24:func.6">Dihedral_group</a> <font color="Olive" title="b1">n</font></span>)</span> holds <br/> ( <font color="Olive" title="b5">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><a href="group_24.html#K6" title="GROUP_24:func.6">Dihedral_group</a> <font color="Olive" title="b1">n</font></span>)</span> iff ( <font color="Olive" title="b5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><a href="group_24.html#K6" title="GROUP_24:func.6">Dihedral_group</a> <font color="Olive" title="b1">n</font></span>)</span> or <font color="Olive" title="b5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">x</font> <a href="group_1.html#K5" title="GROUP_1:func.5">|^</a> <font color="Olive" title="b2">k</font> ) )</div></div>
