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<b>let </b><font color="Maroon">ADG</font> be   <a href="tdgroup.html#NM2">Uniquely_Two_Divisible_Group</a>;<br/>

<b>assume </b><a NAME="E1:27"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">ADG</font> st <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b</font>
 ;<br/>

<a NAME="E2:27"/><b>then </b>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" target="_self">AV</a> <font color="Maroon">ADG</font></span>)</span> st <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b</font> &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" target="_self">AV</a> <font color="Maroon">ADG</font></span>)</span>  st <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">c</font>,<font color="Olive">c</font> holds <br/><font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">d</font>, <font color="Olive">p</font>, <font color="Olive">q</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" target="_self">AV</a> <font color="Maroon">ADG</font></span>)</span>  st <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">p</font>,<font color="Olive">q</font> &amp; <font color="Olive">c</font>,<font color="Olive">d</font> <a href="analoaf.html#R2">//</a> <font color="Olive">p</font>,<font color="Olive">q</font> holds <br/><font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">c</font>,<font color="Olive">d</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" target="_self">AV</a> <font color="Maroon">ADG</font></span>)</span>  ex <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" target="_self">AV</a> <font color="Maroon">ADG</font></span>)</span> st <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">c</font>,<font color="Olive">d</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">a'</font>, <font color="Olive">b'</font>, <font color="Olive">c'</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" target="_self">AV</a> <font color="Maroon">ADG</font></span>)</span>  st <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">b'</font> &amp; <font color="Olive">a</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">c'</font> holds <br/><font color="Olive">b</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b'</font>,<font color="Olive">c'</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" target="_self">AV</a> <font color="Maroon">ADG</font></span>)</span>  ex <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" target="_self">AV</a> <font color="Maroon">ADG</font></span>)</span> st <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">c</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">b'</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" target="_self">AV</a> <font color="Maroon">ADG</font></span>)</span>  st <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">c</font> &amp; <font color="Olive">a</font>,<font color="Olive">b'</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b'</font>,<font color="Olive">c</font> holds <br/><font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">b'</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" target="_self">AV</a> <font color="Maroon">ADG</font></span>)</span>  st <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">c</font>,<font color="Olive">d</font> holds <br/><font color="Olive">a</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">d</font> ) )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:27"/>
 <a href="tdgroup.html#K2" target="_self">AV</a> <font color="Maroon">ADG</font> is   <a href="tdgroup.html#NM3">AffVect</a>
 <b>by </b><i>, <a class="ref" href="realset2.html#D7">REALSET2:def 7</a></i>;<br/>


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