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

<span class="kw">let </span><font color="Maroon" title="c1">ADG</font> be   <a href="tdgroup.html#NM2" title="TDGROUP:NM.2">Uniquely_Two_Divisible_Group</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">ADG</font> st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> implies (  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  ex <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">a9</font>, <font color="Olive" title="b5">b9</font>, <font color="Olive" title="b6">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b6">c9</font> holds <br/><font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b9</font>,<font color="Olive" title="b6">c9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  ex <font color="Olive" title="b3">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">c</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">b9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font> ) ) )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">A</font> =  <a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font>;<br/>
<span class="kw">assume </span><a NAME="E1:27"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">ADG</font> st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  ex <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">a9</font>, <font color="Olive" title="b5">b9</font>, <font color="Olive" title="b6">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b6">c9</font> holds <br/><font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b9</font>,<font color="Olive" title="b6">c9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  ex <font color="Olive" title="b3">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">c</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">b9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font> ) )</span><br/>

<span class="kw">hence </span><a NAME="E2:27"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  ex <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">a9</font>, <font color="Olive" title="b5">b9</font>, <font color="Olive" title="b6">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b6">c9</font> holds <br/><font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b9</font>,<font color="Olive" title="b6">c9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  ex <font color="Olive" title="b3">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">c</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">b9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font> ) )</span><br/>

<a NAME="E3:27"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
 <a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analoaf.html#G1" title="ANALOAF:aggr.1">AffinStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">ADG</font>,<span class="p1">(<span class="default"><a href="tdgroup.html#K1" title="TDGROUP:func.1">CONGRD</a> <font color="Maroon" title="c1">ADG</font></span>)</span> #)
 
;<br/>
<a NAME="E4:27"/><span class="lab"><font color="Green" title="E17">A2</font></span>: 
for <font color="Olive" title="b1">a9</font>, <font color="Olive" title="b2">b9</font>, <font color="Olive" title="b3">c9</font>, <font color="Olive" title="b4">d9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span><br/> for <font color="Olive" title="b5">a</font>, <font color="Olive" title="b6">b</font>, <font color="Olive" title="b7">c</font>, <font color="Olive" title="b8">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">ADG</font>  st <font color="Olive" title="b5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a9</font> &amp; <font color="Olive" title="b6">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b9</font> &amp; <font color="Olive" title="b7">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c9</font> &amp; <font color="Olive" title="b8">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">d9</font> holds <br/>( <font color="Olive" title="b5">a</font>,<font color="Olive" title="b6">b</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Olive" title="b7">c</font>,<font color="Olive" title="b8">d</font> iff <font color="Olive" title="b1">a9</font>,<font color="Olive" title="b2">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c9</font>,<font color="Olive" title="b4">d9</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">a9</font>, <font color="Maroon" title="c4">b9</font>, <font color="Maroon" title="c5">c9</font>, <font color="Maroon" title="c6">d9</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">ADG</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a9</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b9</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c9</font> &amp; <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d9</font> holds <br/>( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> iff <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c9</font>,<font color="Maroon" title="c6">d9</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">b</font>, <font color="Maroon" title="c9">c</font>, <font color="Maroon" title="c10">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">ADG</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a9</font> &amp; <font color="Maroon" title="c8">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b9</font> &amp; <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c9</font> &amp; <font color="Maroon" title="c10">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d9</font> implies ( <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">d</font> iff <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c9</font>,<font color="Maroon" title="c6">d9</font> ) )</span><br/>









<span class="kw">assume </span><a NAME="E1:27_1"/><span class="lab"><font color="Green" title="E18">A3</font></span>: 
( <font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a9</font> &amp; <font color="Maroon" title="c8">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b9</font> &amp; <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c9</font> &amp; <font color="Maroon" title="c10">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d9</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">d</font> iff <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c9</font>,<font color="Maroon" title="c6">d9</font> )</span><br/>

<div><span class="lab"><font color="Green" title="E19">A4</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:27_1_1"/>
<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c9</font>,<font color="Maroon" title="c6">d9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">d</font></span><br/><a NAME="E2:27_1_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">d</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdgroup.html#K1" title="TDGROUP:func.1">CONGRD</a> <font color="Maroon" title="c1">ADG</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="ref" href="analoaf.html#D2" title="ANALOAF:def.2">ANALOAF:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:27_1_1"/>
<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="tdgroup.html#D6" target="_self" title="TDGROUP:def.6">Def6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:27_1_2"/>
<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c9</font>,<font color="Maroon" title="c6">d9</font></span><br/><a NAME="E2:27_1_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">d</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdgroup.html#K1" title="TDGROUP:func.1">CONGRD</a> <font color="Maroon" title="c1">ADG</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="tdgroup.html#D6" target="_self" title="TDGROUP:def.6">Def6</a></span>;<br/><span class="kw">hence </span><a NAME="E3:27_1_2"/>
<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c9</font>,<font color="Maroon" title="c6">d9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="ref" href="analoaf.html#D2" title="ANALOAF:def.2">ANALOAF:def 2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:27_1"/>
( <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">d</font> iff <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c9</font>,<font color="Maroon" title="c6">d9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27_1"><span class="lab"><font color="Green" title="E19">A4</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">thus </span><a NAME="E5:27"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  ex <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">a9</font>, <font color="Olive" title="b5">b9</font>, <font color="Olive" title="b6">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b6">c9</font> holds <br/><font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b9</font>,<font color="Olive" title="b6">c9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  ex <font color="Olive" title="b3">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">c</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">b9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font> ) )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c5">c</font> implies <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:27_2"/><span class="lab"><font color="Green" title="E18">A5</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c5">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">a9</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c7">b9</font> = <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c8">c9</font> = <font color="Maroon" title="c5">c</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">ADG</font> ;<br/>
<a NAME="E3:27_2"/>
<font color="Maroon" title="c6">a9</font>,<font color="Maroon" title="c7">b9</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c8">c9</font>,<font color="Maroon" title="c8">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E1:27_2"><span class="lab"><font color="Green" title="E18">A5</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:27_2"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tdgroup.html#T13" target="_self" title="TDGROUP:th.13">Th13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E6:27"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  ex <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">a9</font>, <font color="Olive" title="b5">b9</font>, <font color="Olive" title="b6">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b6">c9</font> holds <br/><font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b9</font>,<font color="Olive" title="b6">c9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  ex <font color="Olive" title="b3">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">c</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">b9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font> ) )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c6">d</font>, <font color="Maroon" title="c7">p</font>, <font color="Maroon" title="c8">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font> &amp; <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font> implies <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c9">a9</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c10">b9</font> = <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c11">c9</font> = <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c12">d9</font> = <font color="Maroon" title="c6">d</font>, <font color="Maroon" title="c13">p9</font> = <font color="Maroon" title="c7">p</font>, <font color="Maroon" title="c14">q9</font> = <font color="Maroon" title="c8">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">ADG</font> ;<br/>
<span class="kw">assume </span><a NAME="E2:27_3"/>
( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font> &amp; <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font></span><br/>

<a NAME="E3:27_3"/><span class="kw">then </span>
( <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">b9</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c13">p9</font>,<font color="Maroon" title="c14">q9</font> &amp; <font color="Maroon" title="c11">c9</font>,<font color="Maroon" title="c12">d9</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c13">p9</font>,<font color="Maroon" title="c14">q9</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E17">A2</font></span></a></span>;<br/>
<a NAME="E4:27_3"/><span class="kw">then </span>
<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">b9</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c11">c9</font>,<font color="Maroon" title="c12">d9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tdgroup.html#T14" target="_self" title="TDGROUP:th.14">Th14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:27_3"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E17">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E7:27"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  ex <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">a9</font>, <font color="Olive" title="b5">b9</font>, <font color="Olive" title="b6">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b6">c9</font> holds <br/><font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b9</font>,<font color="Olive" title="b6">c9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  ex <font color="Olive" title="b3">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">c</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">b9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font> ) )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Olive" title="b1">d</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">a9</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c7">b9</font> = <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c8">c9</font> = <font color="Maroon" title="c5">c</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">ADG</font> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">d9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">ADG</font><span class="kw"> such that </span><br/><a NAME="E3:27_4"/><span class="lab"><font color="Green" title="E18">A6</font></span>: 
<font color="Maroon" title="c6">a9</font>,<font color="Maroon" title="c7">b9</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c8">c9</font>,<font color="Maroon" title="c9">d9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tdgroup.html#T15" target="_self" title="TDGROUP:th.15">Th15</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">d</font> = <font color="Maroon" title="c9">d9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c10">d</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c10">d</font></span><br/>

<span class="kw">thus </span><a NAME="E5:27_4"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c10">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E3:27_4"><span class="lab"><font color="Green" title="E18">A6</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E8:27"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">a9</font>, <font color="Olive" title="b5">b9</font>, <font color="Olive" title="b6">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b6">c9</font> holds <br/><font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b9</font>,<font color="Olive" title="b6">c9</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  ex <font color="Olive" title="b3">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">c</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">b9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font> ) )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c6">a9</font>, <font color="Maroon" title="c7">b9</font>, <font color="Maroon" title="c8">c9</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a9</font>,<font color="Maroon" title="c7">b9</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a9</font>,<font color="Maroon" title="c8">c9</font> implies <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b9</font>,<font color="Maroon" title="c8">c9</font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c9">p</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c10">q</font> = <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c11">r</font> = <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c12">p9</font> = <font color="Maroon" title="c6">a9</font>, <font color="Maroon" title="c13">q9</font> = <font color="Maroon" title="c7">b9</font>, <font color="Maroon" title="c14">r9</font> = <font color="Maroon" title="c8">c9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">ADG</font> ;<br/>
<span class="kw">assume </span><a NAME="E2:27_5"/>
( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a9</font>,<font color="Maroon" title="c7">b9</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a9</font>,<font color="Maroon" title="c8">c9</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b9</font>,<font color="Maroon" title="c8">c9</font></span><br/>

<a NAME="E3:27_5"/><span class="kw">then </span>
( <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c12">p9</font>,<font color="Maroon" title="c13">q9</font> &amp; <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c11">r</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c12">p9</font>,<font color="Maroon" title="c14">r9</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E17">A2</font></span></a></span>;<br/>
<a NAME="E4:27_5"/><span class="kw">then </span>
<font color="Maroon" title="c10">q</font>,<font color="Maroon" title="c11">r</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c13">q9</font>,<font color="Maroon" title="c14">r9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tdgroup.html#T16" target="_self" title="TDGROUP:th.16">Th16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:27_5"/>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b9</font>,<font color="Maroon" title="c8">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E17">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E9:27"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  ex <font color="Olive" title="b3">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">c</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">b9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font> ) )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> st <font color="Maroon" title="c3">a</font>,<font color="Olive" title="b1">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">b</font>,<font color="Maroon" title="c4">c</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">a9</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c6">c9</font> = <font color="Maroon" title="c4">c</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">ADG</font> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">b9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">ADG</font><span class="kw"> such that </span><br/><a NAME="E3:27_6"/><span class="lab"><font color="Green" title="E18">A7</font></span>: 
<font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c7">b9</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c7">b9</font>,<font color="Maroon" title="c6">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tdgroup.html#T17" target="_self" title="TDGROUP:th.17">Th17</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">b</font> = <font color="Maroon" title="c7">b9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c8">b</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c8">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c4">c</font></span><br/>

<span class="kw">thus </span><a NAME="E5:27_6"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c8">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E3:27_6"><span class="lab"><font color="Green" title="E18">A7</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E10:27"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">b9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b9</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_7"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c6">b9</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b9</font>,<font color="Maroon" title="c5">c</font> implies <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b9</font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">a9</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c8">p</font> = <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c9">c9</font> = <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c10">p9</font> = <font color="Maroon" title="c6">b9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">ADG</font> ;<br/>
<span class="kw">assume </span><a NAME="E2:27_7"/>
( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b9</font>,<font color="Maroon" title="c5">c</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b9</font></span><br/>

<a NAME="E3:27_7"/><span class="kw">then </span>
( <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">p</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c9">c9</font> &amp; <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c10">p9</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c10">p9</font>,<font color="Maroon" title="c9">c9</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E17">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:27_7"/>
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tdgroup.html#T18" target="_self" title="TDGROUP:th.18">Th18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E11:27"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_8"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c6">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2" title="TDGROUP:func.2">AV</a> <font color="Maroon" title="c1">ADG</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font> implies <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">a9</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c8">b9</font> = <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c9">c9</font> = <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c10">d9</font> = <font color="Maroon" title="c6">d</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">ADG</font> ;<br/>
<span class="kw">assume </span><a NAME="E2:27_8"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><br/>

<a NAME="E3:27_8"/><span class="kw">then </span>
<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c10">d9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E17">A2</font></span></a></span>;<br/>
<a NAME="E4:27_8"/><span class="kw">then </span>
<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c9">c9</font> <a href="tdgroup.html#R1" title="TDGROUP:pred.1">==&gt;</a> <font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c10">d9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tdgroup.html#T19" target="_self" title="TDGROUP:th.19">Th19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:27_8"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E17">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>


</div>
