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<b>let </b><font color="Maroon" title="c1">AFP</font> be   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</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">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">p</font>, <font color="Olive" title="b5">q</font>, <font color="Olive" title="b6">p'</font>, <font color="Olive" title="b7">q'</font>, <font color="Olive" title="b8">y</font>, <font color="Olive" title="b9">x'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font>  st <font color="Maroon" title="c1">AFP</font> is <a href="aff_2.html#V11" title="AFF_2:attr.11">translational</a> &amp; <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;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">x</font> &amp; <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">p</font>,<font color="Olive" title="b5">q</font> &amp; <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="b6">p'</font>,<font color="Olive" title="b7">q'</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b5">q</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b6">p'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b7">q'</font> &amp; <font color="Olive" title="b4">p</font>,<font color="Olive" title="b5">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">x</font>,<font color="Olive" title="b8">y</font> &amp; <font color="Olive" title="b4">p</font>,<font color="Olive" title="b3">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">q</font>,<font color="Olive" title="b8">y</font> &amp; <font color="Olive" title="b6">p'</font>,<font color="Olive" title="b7">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b9">x'</font>,<font color="Olive" title="b8">y</font> &amp; <font color="Olive" title="b6">p'</font>,<font color="Olive" title="b9">x'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b7">q'</font>,<font color="Olive" title="b8">y</font> &amp; not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">p</font> &amp; not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b6">p'</font> holds <br/><font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b9">x'</font></span><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">x'</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">AFP</font> is <a href="aff_2.html#V11" title="AFF_2:attr.11">translational</a> &amp; <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> &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="c3">b</font>,<font color="Maroon" title="c4">x</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="c5">p</font>,<font color="Maroon" title="c6">q</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="c7">p'</font>,<font color="Maroon" title="c8">q'</font> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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="c10">x'</font>,<font color="Maroon" title="c9">y</font> &amp; <font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c10">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> &amp; 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> &amp; 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> implies <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">x'</font> )</span><br/>



















<b>assume </b><b>that </b><br/><a NAME="E1:18"/><i><font color="Green" title="E19">A1</font></i>: 
<font color="Maroon" title="c1">AFP</font> is <a href="aff_2.html#V11" title="AFF_2:attr.11">translational</a>
 <b>and </b><br/><a NAME="E2:18"/><i><font color="Green" title="E20">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="E3:18"/><i><font color="Green" title="E21">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="E4:18"/><i><font color="Green" title="E22">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="E5:18"/><i><font color="Green" title="E23">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="E6:18"/><i><font color="Green" title="E24">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="E7:18"/><i><font color="Green" title="E25">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="E8:18"/><i><font color="Green" title="E26">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="E9:18"/><i><font color="Green" title="E27">A9</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="E10:18"/><i><font color="Green" title="E28">A10</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="c10">x'</font>,<font color="Maroon" title="c9">y</font>
 <b>and </b><br/><a NAME="E11:18"/><i><font color="Green" title="E29">A11</font></i>: 
<font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c10">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>and </b><br/><a NAME="E12:18"/><i><font color="Green" title="E30">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="E13:18"/><i><font color="Green" title="E31">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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">x'</font></span><br/>

<a NAME="E14:18"/>
 <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="c9">y</font>
 
<b>by </b><i><a class="txt" href="#E2:18"><i><font color="Green" title="E20">A2</font></i></a>, <a class="txt" href="#E3:18"><i><font color="Green" title="E21">A3</font></i></a>, <a class="txt" href="#E4:18"><i><font color="Green" title="E22">A4</font></i></a>, <a class="txt" href="#E6:18"><i><font color="Green" title="E24">A6</font></i></a>, <a class="txt" href="#E8:18"><i><font color="Green" title="E26">A8</font></i></a>, <a class="txt" href="#E12:18"><i><font color="Green" title="E30">A12</font></i></a>, <a class="txt" href="translac.html#E19"><i><font color="Green" title="E17">Lm10</font></i></a></i>;<br/>
<a NAME="E15:18"/><b>then </b><i><font color="Green" title="E32">A14</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c9">y</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E16:18"/><i><font color="Green" title="E33">A15</font></i>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c5">p</font>
 
<b>by </b><i><a class="txt" href="#E4:18"><i><font color="Green" title="E22">A4</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E17:18"/><i><font color="Green" title="E34">A16</font></i>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">q'</font>,<font color="Maroon" title="c7">p'</font>
 
<b>by </b><i><a class="txt" href="#E5:18"><i><font color="Green" title="E23">A5</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E18:18"/><i><font color="Green" title="E35">A17</font></i>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">p</font>
 
<b>by </b><i><a class="txt" href="#E6:18"><i><font color="Green" title="E24">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="E19:18"/><i><font color="Green" title="E36">A18</font></i>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c8">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c7">p'</font>
 
<b>by </b><i><a class="txt" href="#E7:18"><i><font color="Green" title="E25">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="E20:18"/><i><font color="Green" title="E37">A19</font></i>: 
<font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c5">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c4">x</font>
 
<b>by </b><i><a class="txt" href="#E8:18"><i><font color="Green" title="E26">A8</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E21:18"/><i><font color="Green" title="E38">A20</font></i>: 
<font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c9">y</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="txt" href="#E9:18"><i><font color="Green" title="E27">A9</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E22:18"/><i><font color="Green" title="E39">A21</font></i>: 
<font color="Maroon" title="c8">q'</font>,<font color="Maroon" title="c7">p'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c10">x'</font>
 
<b>by </b><i><a class="txt" href="#E10:18"><i><font color="Green" title="E28">A10</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E23:18"/><i><font color="Green" title="E40">A22</font></i>: 
<font color="Maroon" title="c8">q'</font>,<font color="Maroon" title="c9">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c10">x'</font>
 
<b>by </b><i><a class="txt" href="#E11:18"><i><font color="Green" title="E29">A11</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E24:18"/><i><font color="Green" title="E41">A23</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">q</font>
 
<b>by </b><i><a class="txt" href="#E4:18"><i><font color="Green" title="E22">A4</font></i></a>, <a class="txt" href="#E6:18"><i><font color="Green" title="E24">A6</font></i></a>, <a class="txt" href="#E12:18"><i><font color="Green" title="E30">A12</font></i></a>, <a class="txt" href="translac.html#E10"><i><font color="Green" title="E8">Lm5</font></i></a></i>;<br/>
<a NAME="E25:18"/>
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c8">q'</font>
 
<b>by </b><i><a class="txt" href="#E5:18"><i><font color="Green" title="E23">A5</font></i></a>, <a class="txt" href="#E7:18"><i><font color="Green" title="E25">A7</font></i></a>, <a class="txt" href="#E13:18"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="translac.html#E10"><i><font color="Green" title="E8">Lm5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E26:18"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">x'</font>
 <b>by </b><i><a class="txt" href="#E1:18"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="#E2:18"><i><font color="Green" title="E20">A2</font></i></a>, <a class="txt" href="#E15:18"><i><font color="Green" title="E32">A14</font></i></a>, <a class="txt" href="#E16:18"><i><font color="Green" title="E33">A15</font></i></a>, <a class="txt" href="#E17:18"><i><font color="Green" title="E34">A16</font></i></a>, <a class="txt" href="#E18:18"><i><font color="Green" title="E35">A17</font></i></a>, <a class="txt" href="#E19:18"><i><font color="Green" title="E36">A18</font></i></a>, <a class="txt" href="#E20:18"><i><font color="Green" title="E37">A19</font></i></a>, <a class="txt" href="#E21:18"><i><font color="Green" title="E38">A20</font></i></a>, <a class="txt" href="#E22:18"><i><font color="Green" title="E39">A21</font></i></a>, <a class="txt" href="#E23:18"><i><font color="Green" title="E40">A22</font></i></a>, <a class="txt" href="#E24:18"><i><font color="Green" title="E41">A23</font></i></a>, <a class="txt" href="translac.html#E18"><i><font color="Green" title="E16">Lm9</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/>


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