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<span class="kw">let </span><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</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">H</font> <a href="group_6.html#R1" title="GROUP_6:pred.1">are_isomorphic</a>  implies <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c1">G</font> <a href="group_6.html#R1" title="GROUP_6:pred.1">are_isomorphic</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:96"/>
<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> 
 ; <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">H</font>,<font color="Maroon" title="c1">G</font> <a href="group_6.html#R1" title="GROUP_6:pred.1">are_isomorphic</a> </span><br/>

<span class="kw">then </span><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">H</font><span class="kw"> such that </span><br/><a NAME="E3:96"/><span class="lab"><font color="Green" title="E57">A1</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="ref" href="group_6.html#D15" target="_self" title="GROUP_6:def.15">Def15</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">g</font> = <font color="Maroon" title="c3">h</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  as   <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="c1">G</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:96"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="ref" href="group_6.html#T72" target="_self" title="GROUP_6:th.72">Th72</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">g</font>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="group_6.html#D15" target="_self" title="GROUP_6:def.15">GROUP_6:def 15</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="c4">g</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> </span><br/>

<span class="kw">thus </span><a NAME="E5:96"/>
<font color="Maroon" title="c4">g</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="#E3:96"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="ref" href="group_6.html#T73" target="_self" title="GROUP_6:th.73">Th73</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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