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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E84">DefDihedral</font></span>   defines <a href="group_24.html#K6" title="GROUP_24:func.6">Dihedral_group</a> <a onclick="hs(this)" href="javascript:()">GROUP_24:def 7 : <br/></a><span> for <font color="Olive" title="b1">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="counters.html#NM1" title="COUNTERS:NM.1">ExtNat</a><br/>  for <font color="Olive">b<sub>2</sub></font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a> holds <br/> ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_24.html#K6" title="GROUP_24:func.6">Dihedral_group</a> <font color="Olive" title="b1">n</font> iff ( ( <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a>  implies <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_24.html#K1" title="GROUP_24:func.1">semidirect_product</a> (<a href="gr_cy_1.html#K2" title="GR_CY_1:func.2">INT.Group</a>,<span class="p1">(<span class="default"><a href="gr_cy_1.html#K4" title="GR_CY_1:func.4">INT.Group</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="group_24.html#K5" title="GROUP_24:func.5">inversions</a> <a href="gr_cy_1.html#K2" title="GR_CY_1:func.2">INT.Group</a></span>)</span>) ) &amp; ( <font color="Olive" title="b1">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a>  implies  ex <font color="Olive" title="b3">n1</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 <br/>( <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">n1</font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_24.html#K1" title="GROUP_24:func.1">semidirect_product</a> (<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="b3">n1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gr_cy_1.html#K4" title="GR_CY_1:func.4">INT.Group</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="group_24.html#K5" title="GROUP_24:func.5">inversions</a> <span class="p2">(<span class="default"><a href="gr_cy_1.html#K4" title="GR_CY_1:func.4">INT.Group</a> <font color="Olive" title="b3">n1</font></span>)</span></span>)</span>) ) ) ) );<br/></span></div>
