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<b>let </b><font color="Maroon" title="c1">AFS</font> be   <a href="diraf.html#NM1" title="DIRAF:NM.1">AffinSpace</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>, <font color="Olive" title="b2">g</font> being  <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">AFS</font>  st <font color="Olive" title="b1">f</font> is <a href="transgeo.html#V8" title="TRANSGEO:attr.8">collineation</a> &amp; <font color="Olive" title="b2">g</font> is <a href="transgeo.html#V8" title="TRANSGEO:attr.8">collineation</a> holds <br/>( <font color="Olive" title="b1">f</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a>  is <a href="transgeo.html#V8" title="TRANSGEO:attr.8">collineation</a> &amp; <font color="Olive" title="b1">f</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Olive" title="b2">g</font> is <a href="transgeo.html#V8" title="TRANSGEO:attr.8">collineation</a> &amp;  <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">AFS</font> is <a href="transgeo.html#V8" title="TRANSGEO:attr.8">collineation</a> )</span><br/><b>let </b><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font> be   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">AFS</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> is <a href="transgeo.html#V8" title="TRANSGEO:attr.8">collineation</a> &amp; <font color="Maroon" title="c3">g</font> is <a href="transgeo.html#V8" title="TRANSGEO:attr.8">collineation</a> implies ( <font color="Maroon" title="c2">f</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a>  is <a href="transgeo.html#V8" title="TRANSGEO:attr.8">collineation</a> &amp; <font color="Maroon" title="c2">f</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c3">g</font> is <a href="transgeo.html#V8" title="TRANSGEO:attr.8">collineation</a> &amp;  <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">AFS</font> is <a href="transgeo.html#V8" title="TRANSGEO:attr.8">collineation</a> ) )</span><br/>





<b>assume </b><a NAME="E1:108"/>
( <font color="Maroon" title="c2">f</font> <a href="transgeo.html#R2" title="TRANSGEO:pred.2">is_automorphism_of</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">AFS</font> &amp; <font color="Maroon" title="c3">g</font> <a href="transgeo.html#R2" title="TRANSGEO:pred.2">is_automorphism_of</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">AFS</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="transgeo.html#D12" target="_self" title="TRANSGEO:def.12">TRANSGEO:def 12</a> <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_2.html#K2" title="FUNCT_2:func.2">"</a>  is <a href="transgeo.html#V8" title="TRANSGEO:attr.8">collineation</a> &amp; <font color="Maroon" title="c2">f</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c3">g</font> is <a href="transgeo.html#V8" title="TRANSGEO:attr.8">collineation</a> &amp;  <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">AFS</font> is <a href="transgeo.html#V8" title="TRANSGEO:attr.8">collineation</a> )</span><br/>

<b>hence </b><a NAME="E2:108"/>
( <font color="Maroon" title="c2">f</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a>  <a href="transgeo.html#R2" title="TRANSGEO:pred.2">is_automorphism_of</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">AFS</font> &amp; <font color="Maroon" title="c2">f</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c3">g</font> <a href="transgeo.html#R2" title="TRANSGEO:pred.2">is_automorphism_of</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">AFS</font> )
 <b>by </b><i><a class="ref" href="transgeo.html#T29" target="_self" title="TRANSGEO:th.29">Th29</a>, <a class="ref" href="transgeo.html#T30" target="_self" title="TRANSGEO:th.30">Th30</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="transgeo.html#D12" target="_self" title="TRANSGEO:def.12">TRANSGEO:def 12</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">AFS</font> is <a href="transgeo.html#V8" title="TRANSGEO:attr.8">collineation</a></span><br/>

<b>thus </b><a NAME="E3:108"/>
 <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">AFS</font> <a href="transgeo.html#R2" title="TRANSGEO:pred.2">is_automorphism_of</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">AFS</font>
 <b>by </b><i><a class="ref" href="transgeo.html#T28" target="_self" title="TRANSGEO:th.28">Th28</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="transgeo.html#D12" target="_self" title="TRANSGEO:def.12">TRANSGEO:def 12</a> <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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