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<b>let </b><font color="Maroon" title="c1">G</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><a href="autgroup.html#K3" title="AUTGROUP:func.3">AutGroup</a> <font color="Maroon" title="c1">G</font></span>)</span></span><br/>

<b>reconsider </b><font color="Maroon" title="c2">g</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="autgroup.html#K3" title="AUTGROUP:func.3">AutGroup</a> <font color="Maroon" title="c1">G</font></span>)</span> <b>by </b><i><a class="ref" href="autgroup.html#T4" target="_self" title="AUTGROUP:th.4">Th4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c3">g1</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E3:13"/><i><font color="Green" title="E12">A1</font></i>: 
<font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font>
 ;<br/>
<b>consider </b><font color="Maroon" title="c4">f</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="autgroup.html#K3" title="AUTGROUP:func.3">AutGroup</a> <font color="Maroon" title="c1">G</font></span>)</span>;<br/>
<a NAME="E5:13"/>
<font color="Maroon" title="c4">f</font> is   <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="c1">G</font>
 
<b>by </b><i><a class="ref" href="autgroup.html#D1" target="_self" title="AUTGROUP:def.1">Def1</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">f1</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E7:13"/><i><font color="Green" title="E13">A2</font></i>: 
<font color="Maroon" title="c5">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 ;<br/>
<a NAME="E8:13"/>
( <font color="Maroon" title="c5">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font> implies <font color="Maroon" title="c5">f1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">g</font> )
 
<b>by </b><i><a class="ref" href="autgroup.html#D2" target="_self" title="AUTGROUP:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E9:13"/>
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><a href="autgroup.html#K3" title="AUTGROUP:func.3">AutGroup</a> <font color="Maroon" title="c1">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:13"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</a>, <a class="ref" href="group_1.html#T15" title="GROUP_1:th.15">GROUP_1:15</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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