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<b>let </b><font color="Maroon">G1</font> be   <a href="group_1.html#NM1">Group</a>, <font color="Maroon">G2</font> be   <a href="group_1.html#NM1">Group</a>, <font color="Maroon">H1</font> be   <a href="group_1.html#NM1">Group</a>, <font color="Maroon">H2</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">h1</font> be   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">G1</font>,<font color="Maroon">H1</font>;<br/><b>let </b><font color="Maroon">h2</font> be   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">G2</font>,<font color="Maroon">H2</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:7"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">h1</font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 <b>and </b><br/><a NAME="E2:7"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">h2</font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 ;<br/>

<b>set </b><font color="Maroon">h</font> =  <a href="topalg_4.html#K2" target="_self">Gr2Iso</a> <font color="Maroon">h1</font>,<font color="Maroon">h2</font>;<br/>
<a NAME="E3:7"/>
( <font color="Maroon">h1</font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">h2</font> is <a href="funct_1.html#V2">one-to-one</a> )
 
<b>by </b><i>, , <a class="ref" href="group_6.html#T70">GROUP_6:70</a></i>;<br/>
<a NAME="E4:7"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="topalg_4.html#K2" target="_self">Gr2Iso</a> <font color="Maroon">h1</font>,<font color="Maroon">h2</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i/>;<br/>
<a NAME="E5:7"/>
(  <a href="relset_1.html#K5">rng</a> <font color="Maroon">h1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">h2</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> )
 
<b>by </b><i>, , <a class="ref" href="group_6.html#T70">GROUP_6:70</a></i>;<br/>
<a NAME="E6:7"/><b>then </b>
( <font color="Maroon">h1</font> is <a href="funct_2.html#V2">onto</a> &amp; <font color="Maroon">h2</font> is <a href="funct_2.html#V2">onto</a> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>
<a NAME="E7:7"/><b>then </b>
 <a href="topalg_4.html#K2" target="_self">Gr2Iso</a> <font color="Maroon">h1</font>,<font color="Maroon">h2</font> is <a href="funct_2.html#V2">onto</a>
 
<b>by </b><i/>;<br/>
<a NAME="E8:7"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="topalg_4.html#K2" target="_self">Gr2Iso</a> <font color="Maroon">h1</font>,<font color="Maroon">h2</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2">product</a> <span class="p2"><a href="group_7.html#K15">&lt;*</a><span class="default"><font color="Maroon">H1</font>,<font color="Maroon">H2</font></span><a href="group_7.html#K15">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>
<b>hence </b><a NAME="E9:7"/>
 <a href="topalg_4.html#K2" target="_self">Gr2Iso</a> <font color="Maroon">h1</font>,<font color="Maroon">h2</font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 <b>by </b><i>, <a class="ref" href="group_6.html#T70">GROUP_6:70</a></i>;<br/>


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