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<b>let </b><font color="Maroon" title="c1">AS</font> be  <a href="analoaf.html#V1" title="ANALOAF:attr.1">strict</a>  <a href="analoaf.html#L1" title="ANALOAF:struct.1">AffinStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">AS</font> is   <a href="tdgroup.html#NM3" title="TDGROUP:NM.3">AffVect</a> iff  ex <font color="Olive" title="b1">ADG</font> being  <a href="afvect0.html#NM2" title="AFVECT0:NM.2">Proper_Uniquely_Two_Divisible_Group</a> st <font color="Maroon" title="c1">AS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Olive" title="b1">ADG</font> )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:73_1"/>
<font color="Maroon" title="c1">AS</font> is   <a href="tdgroup.html#NM3" title="TDGROUP:NM.3">AffVect</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">ADG</font> being <a href="algstr_0.html#V8" title="ALGSTR_0:attr.8">strict</a>  <a href="algstr_0.html#L2" title="ALGSTR_0:struct.2">addLoopStr</a>  ex <font color="Olive" title="b2">ADG</font> being  <a href="afvect0.html#NM2" title="AFVECT0:NM.2">Proper_Uniquely_Two_Divisible_Group</a> st <font color="Maroon" title="c1">AS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Olive" title="b2">ADG</font></span><br/><b>then reconsider </b><font color="Maroon" title="c2">AS'</font> = <font color="Maroon" title="c1">AS</font> as   <a href="tdgroup.html#NM3" title="TDGROUP:NM.3">AffVect</a> ;<br/><b>consider </b><font color="Maroon" title="c3">o</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS'</font>;<br/><b>take </b><font color="Maroon" title="c4">ADG</font> =  <a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c2">AS'</font>,<font color="Maroon" title="c3">o</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">ADG</font> being  <a href="afvect0.html#NM2" title="AFVECT0:NM.2">Proper_Uniquely_Two_Divisible_Group</a> st <font color="Maroon" title="c1">AS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Olive" title="b1">ADG</font></span><br/><a NAME="E4:73_1"/>
<font color="Maroon" title="c2">AS'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c4">ADG</font>
 <b>by </b><i><a class="ref" href="afvect0.html#T71" target="_self" title="AFVECT0:th.71">Th71</a></i>;<br/><b>hence </b><a NAME="E5:73_1"/>
 ex <font color="Olive" title="b1">ADG</font> being  <a href="afvect0.html#NM2" title="AFVECT0:NM.2">Proper_Uniquely_Two_Divisible_Group</a> st <font color="Maroon" title="c1">AS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Olive" title="b1">ADG</font>
 ; <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="E2:73"/>
( <font color="Maroon" title="c1">AS</font> is   <a href="tdgroup.html#NM3" title="TDGROUP:NM.3">AffVect</a> iff  ex <font color="Olive" title="b1">ADG</font> being  <a href="afvect0.html#NM2" title="AFVECT0:NM.2">Proper_Uniquely_Two_Divisible_Group</a> st <font color="Maroon" title="c1">AS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Olive" title="b1">ADG</font> )
 ; <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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