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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">Th15</font></span>: <a NAME="T15"><span class="comment"><font color="firebrick">:: GROUP_17:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b2">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">H</font> being   <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b1">G</font>  st  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b4">x</font> where <font color="Olive" title="b4">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">G</font> : <font color="Olive" title="b4">x</font> <a href="group_1.html#K5" title="GROUP_1:func.5">|^</a> <font color="Olive" title="b2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Olive" title="b1">G</font> </span> } </span>  holds <br/> for <font color="Olive" title="b4">q</font> being   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>  st <font color="Olive" title="b4">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#K13" title="NAT_3:func.13">prime_factorization</a> <span class="p2">(<span class="default"><a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Olive" title="b3">H</font></span>)</span></span>)</span> holds <br/> not <font color="Olive" title="b4">q</font>,<font color="Olive" title="b2">m</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a> </div></div>
