<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">ADG</font> be   <a href="tdgroup.html#NM2">Uniquely_Two_Divisible_Group</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">ADG</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">ADG</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">ADG</font>;<br/><b>let </b><font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">ADG</font>;<br/>









<a NAME="E1:14"/><i><font color="Green">E19</font></i>: 
the <a href="analoaf.html#U1">CONGR</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" target="_self">AV</a> <font color="Maroon">ADG</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="tdgroup.html#K1" target="_self">CONGRD</a> <font color="Maroon">ADG</font>
 
;<br/>
<div><i><font color="Green">E20</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_1"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="tdgroup.html#R1" target="_self">==&gt;</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 ;<br/><a NAME="E2:14_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="tdgroup.html#K1" target="_self">CONGRD</a> <font color="Maroon">ADG</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:14_1"/>
<font color="Maroon">a</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">c</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_2"/>
<font color="Maroon">a</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">c</font>
 ;<br/><a NAME="E2:14_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="analoaf.html#U1">CONGR</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" target="_self">AV</a> <font color="Maroon">ADG</font></span>)</span>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:14_2"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="tdgroup.html#R1" target="_self">==&gt;</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:14"/>
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="tdgroup.html#R1" target="_self">==&gt;</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> iff <font color="Maroon">a</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">c</font> )
 <b>by </b><i/>;<br/>


</div>
