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<span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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#R2" title="GROUP_6:pred.2">are_isomorphic</a>  &amp; <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c3">I</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a>  implies <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c3">I</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a>  )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:90"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
<font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> 
 <span class="kw">and </span><br/><a NAME="E2:90"/><span class="lab"><font color="Green" title="E54">A2</font></span>: 
<font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c3">I</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c3">I</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/>

<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E4:90"/><span class="lab"><font color="Green" title="E55">A3</font></span>: 
<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="#E1:90"><span class="lab"><font color="Green" title="E53">A1</font></span></a></span>;<br/>
<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E6:90"/><span class="lab"><font color="Green" title="E56">A4</font></span>: 
<font color="Maroon" title="c5">h1</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="#E2:90"><span class="lab"><font color="Green" title="E54">A2</font></span></a></span>;<br/>
<a NAME="E7:90"/>
<font color="Maroon" title="c5">h1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <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="#E4:90"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="txt" href="#E6:90"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="ref" href="group_6.html#T64" target="_self" onmouseover="rs('group_6/T64')" onmouseout="rh()">Th64</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:90"/>
<font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c3">I</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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