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

<b>let </b><font color="Maroon" title="c1">OAS</font> be   <a href="analoaf.html#NM1" title="ANALOAF:NM.1">OAffinSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font>  st <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">p</font> holds <br/> ex <font color="Olive" title="b5">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>( <font color="Olive" title="b1">p</font>,<font color="Olive" title="b4">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b5">d</font> &amp; <font color="Olive" title="b4">a</font>,<font color="Olive" title="b2">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b5">d</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">d</font> )</span><br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p</font> implies  ex <font color="Olive" title="b1">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">d</font> &amp; <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">d</font> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">d</font> ) )</span><br/>









<b>assume </b><b>that </b><br/><a NAME="E1:14"/><i><font color="Green" title="E3">A1</font></i>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font>
 <b>and </b><br/><a NAME="E2:14"/><i><font color="Green" title="E4">A2</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font>
 <b>and </b><br/><a NAME="E3:14"/><i><font color="Green" title="E5">A3</font></i>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">d</font> &amp; <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">d</font> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">d</font> )</span><br/>

<b>consider </b><font color="Maroon" title="c6">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font><b> such that </b><br/><a NAME="E5:14"/><i><font color="Green" title="E6">A4</font></i>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">q</font>
 <b>and </b><br/><a NAME="E6:14"/><i><font color="Green" title="E7">A5</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q</font>
 <b>by </b><i><a class="ref" href="diraf.html#T17" title="DIRAF:th.17">DIRAF:17</a></i>;<br/>
<a NAME="E7:14"/><i><font color="Green" title="E8">A6</font></i>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">q</font>
 
<b>by </b><i><a class="txt" href="pasch.html#E5:14"><i><font color="Green" title="E6">A4</font></i></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c7">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font><b> such that </b><br/><a NAME="E9:14"/><i><font color="Green" title="E9">A7</font></i>: 
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c7">r</font>
 <b>and </b><br/><a NAME="E10:14"/><i><font color="Green" title="E10">A8</font></i>: 
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c7">r</font>
 <b>and </b><br/><a NAME="E11:14"/><i><font color="Green" title="E11">A9</font></i>: 
<font color="Maroon" title="c6">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">r</font>
 <b>and </b><br/><a NAME="E12:14"/><i><font color="Green" title="E12">A10</font></i>: 
<font color="Maroon" title="c7">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="txt" href="pasch.html#E3:14"><i><font color="Green" title="E5">A3</font></i></a>, <a class="txt" href="pasch.html#E6:14"><i><font color="Green" title="E7">A5</font></i></a>, <a class="ref" href="pasch.html#T7" target="_self" title="PASCH:th.7">Th7</a></i>;<br/>
<a NAME="E13:14"/>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="txt" href="pasch.html#E1:14"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></i>;<br/>
<a NAME="E14:14"/><b>then </b>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="txt" href="pasch.html#E3:14"><i><font color="Green" title="E5">A3</font></i></a>, <a class="txt" href="pasch.html#E7:14"><i><font color="Green" title="E8">A6</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/>
<a NAME="E15:14"/><b>then </b>
<font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c8">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font><b> such that </b><br/><a NAME="E17:14"/><i><font color="Green" title="E13">A11</font></i>: 
<font color="Maroon" title="c7">r</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c8">d</font>
 <b>and </b><br/><a NAME="E18:14"/><i><font color="Green" title="E14">A12</font></i>: 
<font color="Maroon" title="c7">r</font>,<font color="Maroon" title="c6">q</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c8">d</font>
 <b>and </b><br/><a NAME="E19:14"/><i><font color="Green" title="E15">A13</font></i>: 
<font color="Maroon" title="c4">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">d</font>
 <b>and </b><br/><a NAME="E20:14"/>
<font color="Maroon" title="c8">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="txt" href="pasch.html#E2:14"><i><font color="Green" title="E4">A2</font></i></a>, <a class="txt" href="pasch.html#E6:14"><i><font color="Green" title="E7">A5</font></i></a>, <a class="ref" href="pasch.html#T7" target="_self" title="PASCH:th.7">Th7</a></i>;<br/>
<a NAME="E21:14"/>
<font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c7">r</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c8">d</font>
 
<b>by </b><i><a class="txt" href="pasch.html#E18:14"><i><font color="Green" title="E14">A12</font></i></a>, <a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a></i>;<br/>
<a NAME="E22:14"/><b>then </b><i><font color="Green" title="E16">A14</font></i>: 
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c8">d</font>
 
<b>by </b><i><a class="txt" href="pasch.html#E10:14"><i><font color="Green" title="E10">A8</font></i></a>, <a class="txt" href="pasch.html#E11:14"><i><font color="Green" title="E11">A9</font></i></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></i>;<br/>
<a NAME="E23:14"/>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c7">r</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">d</font>,<font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="txt" href="pasch.html#E17:14"><i><font color="Green" title="E13">A11</font></i></a>, <a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></i>;<br/>
<a NAME="E24:14"/><b>then </b>
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">d</font>,<font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="txt" href="pasch.html#E9:14"><i><font color="Green" title="E9">A7</font></i></a>, <a class="txt" href="pasch.html#E12:14"><i><font color="Green" title="E12">A10</font></i></a>, <a class="ref" href="diraf.html#T6" title="DIRAF:th.6">DIRAF:6</a></i>;<br/>
<a NAME="E25:14"/><b>then </b>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c8">d</font>
 
<b>by </b><i><a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></i>;<br/>
<b>hence </b><a NAME="E26:14"/>
 ex <font color="Olive" title="b1">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">d</font> &amp; <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">d</font> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">d</font> )
 <b>by </b><i><a class="txt" href="pasch.html#E19:14"><i><font color="Green" title="E15">A13</font></i></a>, <a class="txt" href="pasch.html#E22:14"><i><font color="Green" title="E16">A14</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
