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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"> for <font color="Olive" title="b1">f</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="autgroup.html#K4" title="AUTGROUP:func.4">InnAut</a> <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b2">g</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#K5" title="AUTGROUP:func.5">InnAutGroup</a> <font color="Maroon" title="c1">G</font></span>)</span>  st <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font> holds <br/><font color="Olive" title="b1">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> </span><br/><b>let </b><font color="Maroon" title="c2">f</font> be    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="autgroup.html#K4" title="AUTGROUP:func.4">InnAut</a> <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"> for <font color="Olive" title="b1">g</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#K5" title="AUTGROUP:func.5">InnAutGroup</a> <font color="Maroon" title="c1">G</font></span>)</span>  st <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> holds <br/><font color="Maroon" title="c2">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> </span><br/><b>let </b><font color="Maroon" title="c3">g</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="autgroup.html#K5" title="AUTGROUP:func.5">InnAutGroup</a> <font color="Maroon" title="c1">G</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> implies <font color="Maroon" title="c2">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  )</span><br/>





<b>assume </b><a NAME="E1:26"/><i><font color="Green" title="E23">A1</font></i>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> </span><br/>

<a NAME="E2:26"/>
<font color="Maroon" title="c2">f</font> is    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="autgroup.html#K1" title="AUTGROUP:func.1">Aut</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="autgroup.html#T13" target="_self" title="AUTGROUP:th.13">Th13</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">f1</font> being    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="autgroup.html#K1" title="AUTGROUP:func.1">Aut</a> <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E4:26"/><i><font color="Green" title="E24">A2</font></i>: 
<font color="Maroon" title="c4">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">f</font>
 ;<br/>
<a NAME="E5:26"/>
<font color="Maroon" title="c3">g</font> is   <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="group_2.html#T51" title="GROUP_2:th.51">GROUP_2:51</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">g1</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><b> such that </b><br/><a NAME="E7:26"/><i><font color="Green" title="E25">A3</font></i>: 
<font color="Maroon" title="c5">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font>
 ;<br/>
<a NAME="E8:26"/>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">g1</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> 
 
<b>by </b><i><a class="txt" href="autgroup.html#E1:26"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="autgroup.html#E4:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="autgroup.html#E7:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="autgroup.html#T11" target="_self" title="AUTGROUP:th.11">Th11</a></i>;<br/>
<b>hence </b><a NAME="E9:26"/>
<font color="Maroon" title="c2">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> 
 <b>by </b><i><a class="txt" href="autgroup.html#E4:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="autgroup.html#E7:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="group_2.html#T57" title="GROUP_2:th.57">GROUP_2:57</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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