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<b>let </b><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</font>, <font color="Maroon" title="c3">I</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font> <a href="group_6.html#R1" title="GROUP_6:pred.1">are_isomorphic</a>  &amp; <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c3">I</font> <a href="group_6.html#R1" title="GROUP_6:pred.1">are_isomorphic</a>  implies <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c3">I</font> <a href="group_6.html#R1" title="GROUP_6:pred.1">are_isomorphic</a>  )</span><br/>





<b>assume </b><b>that </b><br/><a NAME="E1:87"/><i><font color="Green" title="E57">A1</font></i>: 
<font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font> <a href="group_6.html#R1" title="GROUP_6:pred.1">are_isomorphic</a> 
 <b>and </b><br/><a NAME="E2:87"/><i><font color="Green" title="E58">A2</font></i>: 
<font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c3">I</font> <a href="group_6.html#R1" title="GROUP_6:pred.1">are_isomorphic</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c3">I</font> <a href="group_6.html#R1" title="GROUP_6:pred.1">are_isomorphic</a> </span><br/>

<b>consider </b><font color="Maroon" title="c4">g</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">H</font><b> such that </b><br/><a NAME="E4:87"/><i><font color="Green" title="E59">A3</font></i>: 
<font color="Maroon" title="c4">g</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>
 <b>by </b><i><a class="txt" href="#E1:87"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="group_6.html#D15" target="_self" title="GROUP_6:def.15">Def15</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">h1</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c3">I</font><b> such that </b><br/><a NAME="E6:87"/><i><font color="Green" title="E60">A4</font></i>: 
<font color="Maroon" title="c5">h1</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>
 <b>by </b><i><a class="txt" href="#E2:87"><i><font color="Green" title="E58">A2</font></i></a>, <a class="ref" href="group_6.html#D15" target="_self" title="GROUP_6:def.15">Def15</a></i>;<br/>
<a NAME="E7:87"/>
<font color="Maroon" title="c5">h1</font> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <font color="Maroon" title="c4">g</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>
 
<b>by </b><i><a class="txt" href="#E4:87"><i><font color="Green" title="E59">A3</font></i></a>, <a class="txt" href="#E6:87"><i><font color="Green" title="E60">A4</font></i></a>, <a class="ref" href="group_6.html#T74" target="_self" title="GROUP_6:th.74">Th74</a></i>;<br/>
<b>hence </b><a NAME="E8:87"/>
<font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c3">I</font> <a href="group_6.html#R1" title="GROUP_6:pred.1">are_isomorphic</a> 
 <b>by </b><i><a class="ref" href="group_6.html#D15" target="_self" title="GROUP_6:def.15">Def15</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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