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<span class="kw">let </span><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">F</font> be   <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">F</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a>  &amp; <font color="Maroon" title="c1">G</font> is  <a href="gr_cy_1.html#V1" title="GR_CY_1:attr.1">cyclic</a>  implies <font color="Maroon" title="c2">F</font> is  <a href="gr_cy_1.html#V1" title="GR_CY_1:attr.1">cyclic</a>  )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:32"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
<font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">F</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> 
 <span class="kw">and </span><br/><a NAME="E2:32"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
<font color="Maroon" title="c1">G</font> is  <a href="gr_cy_1.html#V1" title="GR_CY_1:attr.1">cyclic</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">F</font> is  <a href="gr_cy_1.html#V1" title="GR_CY_1:attr.1">cyclic</a> </span><br/>

<span class="kw">consider </span><font color="Maroon" title="c3">h</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">F</font><span class="kw"> such that </span><br/><a NAME="E4:32"/><span class="lab"><font color="Green" title="E21">A3</font></span>: 
<font color="Maroon" title="c3">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="group_6.html#D15" title="GROUP_6:def.15">GROUP_6:def 15</a></span>;<br/>
<a NAME="E5:32"/>
<font color="Maroon" title="c3">h</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:32"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="funct_2.html#D4" title="FUNCT_2:def.4">FUNCT_2:def 4</a></span>;<br/>
<a NAME="E6:32"/><span class="kw">then </span>
 <a href="group_6.html#K11" title="GROUP_6:func.11">Image</a> <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T67" title="GROUP_6:th.67">GROUP_6:67</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:32"/>
<font color="Maroon" title="c2">F</font> is  <a href="gr_cy_1.html#V1" title="GR_CY_1:attr.1">cyclic</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="gr_cy_2.html#T32" target="_self" title="GR_CY_2:th.32">Th32</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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