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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"> for <font color="Olive" title="b1">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><br/> for <font color="Olive" title="b2">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> holds <br/> ( <font color="Olive" title="b2">h1</font> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c3">I</font> &amp; <span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c3">I</font></span>)</span> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <font color="Olive" title="b1">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c3">I</font> )</span><br/><b>let </b><font color="Maroon" title="c4">h</font> be   <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">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> holds <br/> ( <font color="Olive" title="b1">h1</font> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c3">I</font> &amp; <span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c3">I</font></span>)</span> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <font color="Maroon" title="c4">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c3">I</font> )</span><br/><b>let </b><font color="Maroon" title="c5">h1</font> be   <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">h1</font> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c3">I</font> &amp; <span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c3">I</font></span>)</span> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <font color="Maroon" title="c4">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c3">I</font> )</span><br/>









<div><i><font color="Green" title="E33">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c3">I</font></span><br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">a</font> = 
<font color="Maroon" title="c5">h1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">a</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
<br/>.= 
<font color="Maroon" title="c5">h1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">H</font></span>)</span>
<b>by </b><i><a class="ref" href="group_6.html#D8" target="_self" title="GROUP_6:def.8">Def8</a></i>
<br/>.= 
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c3">I</font>
<b>by </b><i><a class="ref" href="group_6.html#T40" target="_self" title="GROUP_6:th.40">Th40</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c3">I</font></span>)</span> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c3">I</font></span><br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c3">I</font></span>)</span> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">a</font> = 
<span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c3">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">a</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
<br/>.= 
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c3">I</font>
<b>by </b><i><a class="ref" href="group_6.html#D8" target="_self" title="GROUP_6:def.8">Def8</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:54"/>
( <font color="Maroon" title="c5">h1</font> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c3">I</font> &amp; <span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c3">I</font></span>)</span> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <font color="Maroon" title="c4">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="group_6.html#K8" title="GROUP_6:func.8">1:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c3">I</font> )
 <b>by </b><i><a class="txt" href="group_6.html#E1:54"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="group_6.html#D8" target="_self" title="GROUP_6:def.8">Def8</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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