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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font>, <font color="Maroon" title="c3">H1</font>, <font color="Maroon" title="c4">H2</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">G1</font>,<font color="Maroon" title="c3">H1</font> <a href="group_6.html#R1" title="GROUP_6:pred.1">are_isomorphic</a>  &amp; <font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c4">H2</font> <a href="group_6.html#R1" title="GROUP_6:pred.1">are_isomorphic</a>  implies  <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&lt;*</a><span class="default"><font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font></span><a href="group_7.html#K15" title="GROUP_7:func.15">*&gt;</a></span>, <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&lt;*</a><span class="default"><font color="Maroon" title="c3">H1</font>,<font color="Maroon" title="c4">H2</font></span><a href="group_7.html#K15" title="GROUP_7:func.15">*&gt;</a></span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a>  )</span><br/>

<b>given </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="c1">G1</font>,<font color="Maroon" title="c3">H1</font><b> such that </b><a NAME="E2:8"/><i><font color="Green" title="E9">A1</font></i>: 
<font color="Maroon" title="c5">h1</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="group_6.html#D15" title="GROUP_6:def.15">GROUP_6:def 15</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c4">H2</font> <a href="group_6.html#R1" title="GROUP_6:pred.1">are_isomorphic</a>  or  <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&lt;*</a><span class="default"><font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font></span><a href="group_7.html#K15" title="GROUP_7:func.15">*&gt;</a></span>, <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&lt;*</a><span class="default"><font color="Maroon" title="c3">H1</font>,<font color="Maroon" title="c4">H2</font></span><a href="group_7.html#K15" title="GROUP_7:func.15">*&gt;</a></span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a>  )</span><br/>

<b>given </b><font color="Maroon" title="c6">h2</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c4">H2</font><b> such that </b><a NAME="E4:8"/><i><font color="Green" title="E10">A2</font></i>: 
<font color="Maroon" title="c6">h2</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="group_6.html#D15" title="GROUP_6:def.15">GROUP_6:def 15</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&lt;*</a><span class="default"><font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font></span><a href="group_7.html#K15" title="GROUP_7:func.15">*&gt;</a></span>, <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&lt;*</a><span class="default"><font color="Maroon" title="c3">H1</font>,<font color="Maroon" title="c4">H2</font></span><a href="group_7.html#K15" title="GROUP_7:func.15">*&gt;</a></span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/>

<b>take </b><font color="Maroon" title="c7">h</font> =  <a href="topalg_4.html#K2" title="TOPALG_4:func.2">Gr2Iso</a> <font color="Maroon" title="c5">h1</font>,<font color="Maroon" title="c6">h2</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="group_6.html#D15" title="GROUP_6:def.15">GROUP_6:def 15</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">h</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a></span><br/>

<b>thus </b><a NAME="E5:8"/>
<font color="Maroon" title="c7">h</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>
 <b>by </b><i><a class="txt" href="#E2:8"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E4:8"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="topalg_4.html#T5" target="_self" title="TOPALG_4:th.5">Th5</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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