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

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">OAS</font> is  <a href="papdesaf.html#V6" title="PAPDESAF:attr.6">satisfying_DES_1</a>  implies <font color="Maroon" title="c1">OAS</font> is  <a href="papdesaf.html#V5" title="PAPDESAF:attr.5">satisfying_DES</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:12"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<font color="Maroon" title="c1">OAS</font> is  <a href="papdesaf.html#V6" title="PAPDESAF:attr.6">satisfying_DES_1</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">OAS</font> is  <a href="papdesaf.html#V5" title="PAPDESAF:attr.5">satisfying_DES</a> </span><br/>

<a NAME="E2:12"/>
 for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">a1</font>, <font color="Olive" title="b6">b1</font>, <font color="Olive" title="b7">c1</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">o</font>,<font color="Olive" title="b2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">a1</font> &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b6">b1</font> &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b7">c1</font> &amp;  not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> &amp;  not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">c</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">a1</font>,<font color="Olive" title="b6">b1</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">a1</font>,<font color="Olive" title="b7">c1</font> holds <br/><font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">b1</font>,<font color="Olive" title="b7">c1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">o</font>, <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">a1</font>, <font color="Maroon" title="c7">b1</font>, <font color="Maroon" title="c8">c1</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> &amp;  not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> &amp;  not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> &amp; <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">a1</font>,<font color="Maroon" title="c7">b1</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">a1</font>,<font color="Maroon" title="c8">c1</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">b1</font>,<font color="Maroon" title="c8">c1</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:12_1"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a1</font>
 <span class="kw">and </span><br/><a NAME="E2:12_1"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b1</font>
 <span class="kw">and </span><br/><a NAME="E3:12_1"/><span class="lab"><font color="Green" title="E16">A4</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font>
 <span class="kw">and </span><br/><a NAME="E4:12_1"/><span class="lab"><font color="Green" title="E17">A5</font></span>: 
 not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 <span class="kw">and </span><br/><a NAME="E5:12_1"/><span class="lab"><font color="Green" title="E18">A6</font></span>: 
 not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font>
 <span class="kw">and </span><br/><a NAME="E6:12_1"/><span class="lab"><font color="Green" title="E19">A7</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="c6">a1</font>,<font color="Maroon" title="c7">b1</font>
 <span class="kw">and </span><br/><a NAME="E7:12_1"/><span class="lab"><font color="Green" title="E20">A8</font></span>: 
<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">a1</font>,<font color="Maroon" title="c8">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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">b1</font>,<font color="Maroon" title="c8">c1</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c9">a2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font><span class="kw"> such that </span><br/><a NAME="E9:12_1"/><span class="lab"><font color="Green" title="E21">A9</font></span>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font>
 <span class="kw">and </span><br/><a NAME="E10:12_1"/><span class="lab"><font color="Green" title="E22">A10</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T13" title="DIRAF:th.13">DIRAF:13</a></span>;<br/>
<a NAME="E11:12_1"/><span class="lab"><font color="Green" title="E23">A11</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:12_1"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<a NAME="E12:12_1"/><span class="lab"><font color="Green" title="E24">A12</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:12_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">c2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font><span class="kw"> such that </span><br/><a NAME="E14:12_1"/><span class="lab"><font color="Green" title="E25">A13</font></span>: 
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c10">c2</font>
 <span class="kw">and </span><br/><a NAME="E15:12_1"/><span class="lab"><font color="Green" title="E26">A14</font></span>: 
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c10">c2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:12_1"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/>
<a NAME="E16:12_1"/><span class="lab"><font color="Green" title="E27">A15</font></span>: 
<font color="Maroon" title="c10">c2</font>,<font color="Maroon" title="c9">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:12_1"><span class="lab"><font color="Green" title="E26">A14</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E17:12_1"/><span class="lab"><font color="Green" title="E28">A16</font></span>: 
<font color="Maroon" title="c10">c2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:12_1"><span class="lab"><font color="Green" title="E25">A13</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E18:12_1"/><span class="kw">then </span>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c10">c2</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<a NAME="E19:12_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A17</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c10">c2</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></span>;<br/>
<a NAME="E20:12_1"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:12_1"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></span>;<br/>
<a NAME="E21:12_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A18</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T30" title="DIRAF:th.30">DIRAF:30</a></span>;<br/>
<a NAME="E22:12_1"/><span class="lab"><font color="Green" title="E31">A19</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">c2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:12_1_1"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">c2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:12_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:12_1"><span class="lab"><font color="Green" title="E26">A14</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E3:12_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D4" title="DIRAF:def.4">DIRAF:def 4</a></span>;<br/>
<a NAME="E4:12_1_1"/><span class="kw">then </span>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c2">o</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c5">c</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:12_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E21:12_1"><span class="lab"><font color="Green" title="E30">A18</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a>, <a class="ref" href="diraf.html#T33" title="DIRAF:th.33">DIRAF:33</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:12_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:12_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E10:12_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E21:12_1"><span class="lab"><font color="Green" title="E30">A18</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E23:12_1"/><span class="lab"><font color="Green" title="E32">A20</font></span>: 
 not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c10">c2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:12_1_2"/><span class="lab"><font color="Green" title="E33">A21</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c10">c2</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<a NAME="E2:12_1_2"/><span class="lab"><font color="Green" title="E34">A22</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:12_1_2"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c10">c2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:12_1_2"/><span class="kw">then </span>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c10">c2</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:12_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E21:12_1"><span class="lab"><font color="Green" title="E30">A18</font></span></a>, <a class="txt" href="#E2:12_1_2"><span class="lab"><font color="Green" title="E34">A22</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:12_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:12_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E19:12_1"><span class="lab"><font color="Green" title="E29">A17</font></span></a>, <a class="txt" href="#E22:12_1"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="txt" href="#E1:12_1_2"><span class="lab"><font color="Green" title="E33">A21</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">consider </span><font color="Maroon" title="c11">b2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font><span class="kw"> such that </span><br/><a NAME="E25:12_1"/><span class="lab"><font color="Green" title="E33">A23</font></span>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c11">b2</font>
 <span class="kw">and </span><br/><a NAME="E26:12_1"/><span class="lab"><font color="Green" title="E34">A24</font></span>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c11">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:12_1"><span class="lab"><font color="Green" title="E24">A12</font></span></a>, <a class="txt" href="#E11:12_1"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/>
<a NAME="E27:12_1"/><span class="lab"><font color="Green" title="E35">A25</font></span>: 
<font color="Maroon" title="c11">b2</font>,<font color="Maroon" title="c9">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:12_1"><span class="lab"><font color="Green" title="E34">A24</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E28:12_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:12_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<a NAME="E29:12_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">b2</font>,<font color="Maroon" title="c9">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a1</font>,<font color="Maroon" title="c7">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:12_1"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E27:12_1"><span class="lab"><font color="Green" title="E35">A25</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E30:12_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A26</font></span>: 
<font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c11">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c6">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E31:12_1"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:12_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<a NAME="E32:12_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A27</font></span>: 
<font color="Maroon" title="c10">c2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E17:12_1"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E33:12_1"/><span class="lab"><font color="Green" title="E38">A28</font></span>: 
<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="c10">c2</font>,<font color="Maroon" title="c9">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:12_1"><span class="lab"><font color="Green" title="E26">A14</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/>
<a NAME="E34:12_1"/><span class="lab"><font color="Green" title="E39">A29</font></span>: 
<font color="Maroon" title="c11">b2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:12_1"><span class="lab"><font color="Green" title="E33">A23</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E35:12_1"/><span class="kw">then </span>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c11">b2</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<a NAME="E36:12_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A30</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c11">b2</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></span>;<br/>
<a NAME="E37:12_1"/><span class="lab"><font color="Green" title="E41">A31</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">b2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:12_1_3"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:12_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:12_1"><span class="lab"><font color="Green" title="E34">A24</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E3:12_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D4" title="DIRAF:def.4">DIRAF:def 4</a></span>;<br/>
<a NAME="E4:12_1_3"/><span class="kw">then </span>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c2">o</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c4">b</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:12_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E21:12_1"><span class="lab"><font color="Green" title="E30">A18</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a>, <a class="ref" href="diraf.html#T33" title="DIRAF:th.33">DIRAF:33</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:12_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:12_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E10:12_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E21:12_1"><span class="lab"><font color="Green" title="E30">A18</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E38:12_1"/><span class="lab"><font color="Green" title="E42">A32</font></span>: 
 not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c11">b2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_4"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:12_1_4"/><span class="lab"><font color="Green" title="E43">A33</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c11">b2</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<a NAME="E2:12_1_4"/><span class="lab"><font color="Green" title="E44">A34</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:12_1_4"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c11">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:12_1_4"/><span class="kw">then </span>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c11">b2</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:12_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E21:12_1"><span class="lab"><font color="Green" title="E30">A18</font></span></a>, <a class="txt" href="#E2:12_1_4"><span class="lab"><font color="Green" title="E44">A34</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:12_1_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:12_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E36:12_1"><span class="lab"><font color="Green" title="E40">A30</font></span></a>, <a class="txt" href="#E37:12_1"><span class="lab"><font color="Green" title="E41">A31</font></span></a>, <a class="txt" href="#E1:12_1_4"><span class="lab"><font color="Green" title="E43">A33</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E43">A35</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_5"><span class="kw">now </span></a><div class="add"><a NAME="E1:12_1_5"/>
<font color="Maroon" title="c11">b2</font>,<font color="Maroon" title="c9">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:12_1"><span class="lab"><font color="Green" title="E34">A24</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/><a NAME="E2:12_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A36</font></span>: 
<font color="Maroon" title="c11">b2</font>,<font color="Maroon" title="c9">a2</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D4" title="DIRAF:def.4">DIRAF:def 4</a></span>;<br/><span class="kw">assume </span><a NAME="E3:12_1_5"/><span class="lab"><font color="Green" title="E45">A37</font></span>: 
<font color="Maroon" title="c10">c2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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">b1</font>,<font color="Maroon" title="c8">c1</font></span><br/><a NAME="E4:12_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A38</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c11">b2</font>,<font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:12_1"><span class="lab"><font color="Green" title="E29">A17</font></span></a>, <a class="ref" href="diraf.html#T30" title="DIRAF:th.30">DIRAF:30</a></span>;<br/><a NAME="E5:12_1_5"/>
<font color="Maroon" title="c10">c2</font>,<font color="Maroon" title="c9">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:12_1"><span class="lab"><font color="Green" title="E26">A14</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/><a NAME="E6:12_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A39</font></span>: 
<font color="Maroon" title="c11">b2</font>,<font color="Maroon" title="c9">a2</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1_5"><span class="lab"><font color="Green" title="E45">A37</font></span></a>, <a class="ref" href="diraf.html#D4" title="DIRAF:def.4">DIRAF:def 4</a></span>;<br/><a NAME="E7:12_1_5"/>
(  not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c11">b2</font>,<font color="Maroon" title="c9">a2</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c11">b2</font>,<font color="Maroon" title="c4">b</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:12_1"><span class="lab"><font color="Green" title="E40">A30</font></span></a>, <a class="txt" href="#E38:12_1"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="diraf.html#T30" title="DIRAF:th.30">DIRAF:30</a></span>;<br/><a NAME="E8:12_1_5"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:12_1"><span class="lab"><font color="Green" title="E30">A18</font></span></a>, <a class="txt" href="#E4:12_1_5"><span class="lab"><font color="Green" title="E46">A38</font></span></a>, <a class="txt" href="#E2:12_1_5"><span class="lab"><font color="Green" title="E44">A36</font></span></a>, <a class="txt" href="#E6:12_1_5"><span class="lab"><font color="Green" title="E47">A39</font></span></a>, <a class="ref" href="pasch.html#T4" title="PASCH:th.4">PASCH:4</a></span>;<br/><span class="kw">hence </span><a NAME="E9:12_1_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">b1</font>,<font color="Maroon" title="c8">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T4" title="DIRAF:th.4">DIRAF:4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E40:12_1"/>
<font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:12_1"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E41:12_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A40</font></span>: 
<font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E12:12_1"><span class="lab"><font color="Green" title="E24">A12</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E42:12_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:12_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<a NAME="E43:12_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">c2</font>,<font color="Maroon" title="c9">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a1</font>,<font color="Maroon" title="c8">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:12_1"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="txt" href="#E16:12_1"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E44:12_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A41</font></span>: 
<font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c10">c2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c6">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E45:12_1"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:12_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<a NAME="E46:12_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">b2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E34:12_1"><span class="lab"><font color="Green" title="E39">A29</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E47:12_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A42</font></span>: 
<font color="Maroon" title="c10">c2</font>,<font color="Maroon" title="c11">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E41:12_1"><span class="lab"><font color="Green" title="E44">A40</font></span></a>, <a class="txt" href="#E32:12_1"><span class="lab"><font color="Green" title="E37">A27</font></span></a>, <a class="txt" href="#E44:12_1"><span class="lab"><font color="Green" title="E45">A41</font></span></a>, <a class="txt" href="#E30:12_1"><span class="lab"><font color="Green" title="E36">A26</font></span></a>, <a class="txt" href="#E38:12_1"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="txt" href="#E23:12_1"><span class="lab"><font color="Green" title="E32">A20</font></span></a>, <a class="ref" href="papdesaf.html#D7" target="_self" title="PAPDESAF:def.7">Def16</a></span>;<br/>
<a NAME="E48:12_1"/>
<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="c11">b2</font>,<font color="Maroon" title="c9">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:12_1"><span class="lab"><font color="Green" title="E34">A24</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/>
<a NAME="E49:12_1"/><span class="kw">then </span>
<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="c10">c2</font>,<font color="Maroon" title="c11">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E4:12_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E5:12_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E11:12_1"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="txt" href="#E25:12_1"><span class="lab"><font color="Green" title="E33">A23</font></span></a>, <a class="txt" href="#E14:12_1"><span class="lab"><font color="Green" title="E25">A13</font></span></a>, <a class="txt" href="#E33:12_1"><span class="lab"><font color="Green" title="E38">A28</font></span></a>, <a class="ref" href="papdesaf.html#D7" target="_self" title="PAPDESAF:def.7">Def16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E50:12_1"/>
<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">b1</font>,<font color="Maroon" title="c8">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E47:12_1"><span class="lab"><font color="Green" title="E46">A42</font></span></a>, <a class="txt" href="#E39:12_1"><span class="lab"><font color="Green" title="E43">A35</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:12"/>
<font color="Maroon" title="c1">OAS</font> is  <a href="papdesaf.html#V5" title="PAPDESAF:attr.5">satisfying_DES</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="papdesaf.html#D6" target="_self" title="PAPDESAF:def.6">Def15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
