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<div class="add">

<b>let </b><font color="Maroon" title="c1">AFP</font> be   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">p</font>, <font color="Maroon" title="c6">q</font>, <font color="Maroon" title="c7">p'</font>, <font color="Maroon" title="c8">q'</font>, <font color="Maroon" title="c9">y</font>, <font color="Maroon" title="c10">y'</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font>;<br/>



















<b>assume </b><b>that </b><br/><a NAME="E1:15"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c1">AFP</font> <a href="aff_2.html#NR11" title="AFF_2:NR.11">satisfies_des</a> 
 <b>and </b><br/><a NAME="E2:15"/><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font>
 <b>and </b><br/><a NAME="E3:15"/><i><font color="Green" title="E17">A3</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">x</font>
 <b>and </b><br/><a NAME="E4:15"/><i><font color="Green" title="E18">A4</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font>
 <b>and </b><br/><a NAME="E5:15"/><i><font color="Green" title="E19">A5</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">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>
 <b>and </b><br/><a NAME="E6:15"/><i><font color="Green" title="E20">A6</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">q</font>
 <b>and </b><br/><a NAME="E7:15"/><i><font color="Green" title="E21">A7</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c7">p'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c8">q'</font>
 <b>and </b><br/><a NAME="E8:15"/><i><font color="Green" title="E22">A8</font></i>: 
<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c9">y</font>
 <b>and </b><br/><a NAME="E9:15"/><i><font color="Green" title="E23">A9</font></i>: 
<font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c8">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c10">y'</font>
 <b>and </b><br/><a NAME="E10:15"/><i><font color="Green" title="E24">A10</font></i>: 
<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c4">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c9">y</font>
 <b>and </b><br/><a NAME="E11:15"/><i><font color="Green" title="E25">A11</font></i>: 
<font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c4">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">q'</font>,<font color="Maroon" title="c10">y'</font>
 <b>and </b><br/><a NAME="E12:15"/><i><font color="Green" title="E26">A12</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">p</font>
 <b>and </b><br/><a NAME="E13:15"/><i><font color="Green" title="E27">A13</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">p'</font>
 <b>and </b><br/><a NAME="E14:15"/><i><font color="Green" title="E28">A14</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c7">p'</font>
 ;<br/>

<a NAME="E15:15"/><i><font color="Green" title="E29">A15</font></i>: 
<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c7">p'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c8">q'</font>
 
<b>by </b><i><a class="txt" href="translac.html#E1:15"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="translac.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="translac.html#E5:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="translac.html#E6:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="txt" href="translac.html#E7:15"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="translac.html#E12:15"><i><font color="Green" title="E26">A12</font></i></a>, <a class="txt" href="translac.html#E13:15"><i><font color="Green" title="E27">A13</font></i></a>, <a class="ref" href="translac.html#T6" target="_self" title="TRANSLAC:th.6">Th6</a></i>;<br/>
<a NAME="E16:15"/><i><font color="Green" title="E30">A16</font></i>: 
<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</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>
 
<b>by </b><i><a class="txt" href="translac.html#E2:15"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="translac.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="translac.html#E5:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E17:15"/><i><font color="Green" title="E31">A17</font></i>: 
<font color="Maroon" title="c5">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q</font>
 ;<br/>

<a NAME="E2:15_1"/><b>then </b>
<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="translac.html#E6:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E3:15_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:15_1"/>
contradiction
 <b>by </b><i><a class="txt" href="translac.html#E12:15"><i><font color="Green" title="E26">A12</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E18:15"/><i><font color="Green" title="E32">A18</font></i>: 
<font color="Maroon" title="c7">p'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">q'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2"/>
<font color="Maroon" title="c7">p'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q'</font>
 ;<br/>

<a NAME="E2:15_2"/><b>then </b>
<font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="translac.html#E7:15"><i><font color="Green" title="E21">A7</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E3:15_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:15_2"/>
contradiction
 <b>by </b><i><a class="txt" href="translac.html#E13:15"><i><font color="Green" title="E27">A13</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E19:15"/>
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c4">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_3"/><i><font color="Green" title="E33">A19</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c4">x</font>
 ;<br/>

<a NAME="E2:15_3"/><b>then </b><i><font color="Green" title="E34">A20</font></i>: 
<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c4">x</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E3:15_3"/><i><font color="Green" title="E35">A21</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="translac.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="translac.html#E6:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="txt" href="translac.html#E12:15"><i><font color="Green" title="E26">A12</font></i></a>, <a class="txt" href="translac.html#E1:15_3"><i><font color="Green" title="E33">A19</font></i></a>, <a class="txt" href="translac.html#E10"><i><font color="Green" title="E8">Lm5</font></i></a></i>;<br/>
<a NAME="E4:15_3"/>
( <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c4">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">x</font> )
 
<b>by </b><i><a class="txt" href="translac.html#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="translac.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="translac.html#E17:15"><i><font color="Green" title="E31">A17</font></i></a>, <a class="txt" href="translac.html#E2:15_3"><i><font color="Green" title="E34">A20</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:15_3"/><b>then </b>
<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c4">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">x</font>
 
<b>by </b><i><a class="txt" href="translac.html#E2:15"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E6:15_3"/><b>then </b>
<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E7:15_3"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">a</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c4">x</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="txt" href="translac.html#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:15_3"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">a</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">b</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c5">p</font> )
 
<b>by </b><i><a class="txt" href="translac.html#E3:15_3"><i><font color="Green" title="E35">A21</font></i></a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a>, <a class="ref" href="aff_1.html#T20" title="AFF_1:th.20">AFF_1:20</a></i>;<br/>
<b>hence </b><a NAME="E9:15_3"/>
contradiction
 <b>by </b><i><a class="txt" href="translac.html#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="translac.html#E12:15"><i><font color="Green" title="E26">A12</font></i></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E20:15"/><b>then </b><i><font color="Green" title="E33">A22</font></i>: 
<font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c4">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">q'</font>,<font color="Maroon" title="c9">y</font>
 
<b>by </b><i><a class="txt" href="translac.html#E1:15"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="translac.html#E8:15"><i><font color="Green" title="E22">A8</font></i></a>, <a class="txt" href="translac.html#E10:15"><i><font color="Green" title="E24">A10</font></i></a>, <a class="txt" href="translac.html#E14:15"><i><font color="Green" title="E28">A14</font></i></a>, <a class="txt" href="translac.html#E15:15"><i><font color="Green" title="E29">A15</font></i></a>, <a class="txt" href="translac.html#E16:15"><i><font color="Green" title="E30">A16</font></i></a>, <a class="ref" href="translac.html#T6" target="_self" title="TRANSLAC:th.6">Th6</a></i>;<br/>
<a NAME="E21:15"/><i><font color="Green" title="E34">A23</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c8">q'</font>,<font color="Maroon" title="c4">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_4"/><i><font color="Green" title="E35">A24</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c8">q'</font>,<font color="Maroon" title="c4">x</font>
 ;<br/>

<a NAME="E2:15_4"/><b>then </b><i><font color="Green" title="E36">A25</font></i>: 
<font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c8">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c4">x</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E3:15_4"/><i><font color="Green" title="E37">A26</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="translac.html#E5:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="translac.html#E7:15"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="translac.html#E13:15"><i><font color="Green" title="E27">A13</font></i></a>, <a class="txt" href="translac.html#E1:15_4"><i><font color="Green" title="E35">A24</font></i></a>, <a class="txt" href="translac.html#E10"><i><font color="Green" title="E8">Lm5</font></i></a></i>;<br/>
<a NAME="E4:15_4"/>
( <font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c4">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">x</font> )
 
<b>by </b><i><a class="txt" href="translac.html#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="translac.html#E5:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="translac.html#E18:15"><i><font color="Green" title="E32">A18</font></i></a>, <a class="txt" href="translac.html#E2:15_4"><i><font color="Green" title="E36">A25</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:15_4"/><b>then </b>
<font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c4">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">x</font>
 
<b>by </b><i><a class="txt" href="translac.html#E2:15"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E6:15_4"/><b>then </b>
<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">p'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E7:15_4"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c2">a</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c4">x</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="txt" href="translac.html#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:15_4"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c2">a</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c3">b</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c7">p'</font> )
 
<b>by </b><i><a class="txt" href="translac.html#E3:15_4"><i><font color="Green" title="E37">A26</font></i></a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a>, <a class="ref" href="aff_1.html#T20" title="AFF_1:th.20">AFF_1:20</a></i>;<br/>
<b>hence </b><a NAME="E9:15_4"/>
contradiction
 <b>by </b><i><a class="txt" href="translac.html#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="translac.html#E13:15"><i><font color="Green" title="E27">A13</font></i></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E22:15"/>
<font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c8">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c9">y</font>
 
<b>by </b><i><a class="txt" href="translac.html#E8:15"><i><font color="Green" title="E22">A8</font></i></a>, <a class="txt" href="translac.html#E16:15"><i><font color="Green" title="E30">A16</font></i></a>, <a class="txt" href="translac.html#E17:15"><i><font color="Green" title="E31">A17</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E23:15"/>
<font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">y'</font>
 <b>by </b><i><a class="txt" href="translac.html#E9:15"><i><font color="Green" title="E23">A9</font></i></a>, <a class="txt" href="translac.html#E11:15"><i><font color="Green" title="E25">A11</font></i></a>, <a class="txt" href="translac.html#E20:15"><i><font color="Green" title="E33">A22</font></i></a>, <a class="txt" href="translac.html#E21:15"><i><font color="Green" title="E34">A23</font></i></a>, <a class="ref" href="transgeo.html#T97" title="TRANSGEO:th.97">TRANSGEO:97</a></i>;<br/>


</div>
