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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">p</font>, <font color="Olive" title="b5">p9</font>, <font color="Olive" title="b6">y</font>, <font color="Olive" title="b7">q</font>, <font color="Olive" title="b8">q9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font><br/>  for <font color="Olive" title="b9">K</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AFP</font>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Olive" title="b9">K</font> &amp;  not <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">K</font> &amp;  not <font color="Olive" title="b3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">K</font> &amp; <font color="Maroon" title="c1">AFP</font> is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a>  &amp; <font color="Olive" title="b4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">K</font> &amp; <font color="Olive" title="b5">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">K</font> &amp; <font color="Olive" title="b4">p</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">p9</font>,<font color="Olive" title="b3">x</font> &amp; <font color="Olive" title="b4">p</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">p9</font>,<font color="Olive" title="b6">y</font> &amp; <font color="Olive" title="b3">x</font>,<font color="Olive" title="b6">y</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Olive" title="b9">K</font> &amp; <font color="Olive" title="b7">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">K</font> &amp; <font color="Olive" title="b8">q9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">K</font> &amp; <font color="Olive" title="b7">q</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b8">q9</font>,<font color="Olive" title="b3">x</font> holds <br/><font color="Olive" title="b7">q</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b8">q9</font>,<font color="Olive" title="b6">y</font></span><br/><span class="kw">let </span><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">p9</font>, <font color="Maroon" title="c7">y</font>, <font color="Maroon" title="c8">q</font>, <font color="Maroon" title="c9">q9</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">K</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AFP</font>  st <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Olive" title="b1">K</font> &amp;  not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp;  not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c1">AFP</font> is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a>  &amp; <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c6">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; <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="c6">p9</font>,<font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p9</font>,<font color="Maroon" title="c7">y</font> &amp; <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">y</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c8">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c9">q9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c4">x</font> holds <br/><font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c7">y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c10">K</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AFP</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">a</font>,<font color="Maroon" title="c3">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c10">K</font> &amp;  not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font> &amp;  not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font> &amp; <font color="Maroon" title="c1">AFP</font> is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a>  &amp; <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font> &amp; <font color="Maroon" title="c6">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font> &amp; <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="c6">p9</font>,<font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p9</font>,<font color="Maroon" title="c7">y</font> &amp; <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">y</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c10">K</font> &amp; <font color="Maroon" title="c8">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font> &amp; <font color="Maroon" title="c9">q9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font> &amp; <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c4">x</font> implies <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c7">y</font> )</span><br/>



















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:28"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c10">K</font>
 <span class="kw">and </span><br/><a NAME="E2:28"/><span class="lab"><font color="Green" title="E30">A2</font></span>: 
 not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font>
 <span class="kw">and </span><br/><a NAME="E3:28"/><span class="lab"><font color="Green" title="E31">A3</font></span>: 
 not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font>
 <span class="kw">and </span><br/><a NAME="E4:28"/><span class="lab"><font color="Green" title="E32">A4</font></span>: 
<font color="Maroon" title="c1">AFP</font> is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a> 
 <span class="kw">and </span><br/><a NAME="E5:28"/><span class="lab"><font color="Green" title="E33">A5</font></span>: 
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font>
 <span class="kw">and </span><br/><a NAME="E6:28"/><span class="lab"><font color="Green" title="E34">A6</font></span>: 
<font color="Maroon" title="c6">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font>
 <span class="kw">and </span><br/><a NAME="E7:28"/><span class="lab"><font color="Green" title="E35">A7</font></span>: 
<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="c6">p9</font>,<font color="Maroon" title="c4">x</font>
 <span class="kw">and </span><br/><a NAME="E8:28"/><span class="lab"><font color="Green" title="E36">A8</font></span>: 
<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p9</font>,<font color="Maroon" title="c7">y</font>
 <span class="kw">and </span><br/><a NAME="E9:28"/><span class="lab"><font color="Green" title="E37">A9</font></span>: 
<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">y</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c10">K</font>
 <span class="kw">and </span><br/><a NAME="E10:28"/><span class="lab"><font color="Green" title="E38">A10</font></span>: 
<font color="Maroon" title="c8">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font>
 <span class="kw">and </span><br/><a NAME="E11:28"/><span class="lab"><font color="Green" title="E39">A11</font></span>: 
<font color="Maroon" title="c9">q9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font>
 <span class="kw">and </span><br/><a NAME="E12:28"/><span class="lab"><font color="Green" title="E40">A12</font></span>: 
<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c4">x</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="c8">q</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c7">y</font></span><br/>

<a NAME="E13:28"/><span class="lab"><font color="Green" title="E41">A13</font></span>: 
<font color="Maroon" title="c10">K</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E42">A14</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:28_1"/><span class="lab"><font color="Green" title="E43">A15</font></span>: 
<font color="Maroon" title="c2">a</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">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:28"><span class="lab"><font color="Green" title="E40">A12</font></span></a>, <a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><a NAME="E2:28_1"/><span class="lab"><font color="Green" title="E44">A16</font></span>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c6">p9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:28"><span class="lab"><font color="Green" title="E36">A8</font></span></a>, <a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><a NAME="E3:28_1"/><span class="lab"><font color="Green" title="E45">A17</font></span>: 
<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="c4">x</font>,<font color="Maroon" title="c6">p9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c11">A</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">x</font>);<br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E4:28_1"/><span class="lab"><font color="Green" title="E46">A18</font></span>: 
 not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">x</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c10">K</font>
 <span class="kw">and </span><br/><a NAME="E5:28_1"/><span class="lab"><font color="Green" title="E47">A19</font></span>: 
<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>
 ; <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="c8">q</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c7">y</font></span><br/><a NAME="E6:28_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:28"><span class="lab"><font color="Green" title="E41">A13</font></span></a>, <a class="txt" href="#E4:28_1"><span class="lab"><font color="Green" title="E46">A18</font></span></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/><a NAME="E7:28_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A20</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">x</font>) is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D3" title="AFF_1:def.3">AFF_1:def 3</a></span>;<br/><a NAME="E8:28_1"/><span class="lab"><font color="Green" title="E49">A21</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">x</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E9:28_1"/><span class="lab"><font color="Green" title="E50">A22</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">x</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">o</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font><span class="kw"> such that </span><br/><a NAME="E11:28_1"/><span class="lab"><font color="Green" title="E51">A23</font></span>: 
<font color="Maroon" title="c12">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">x</font>)
 <span class="kw">and </span><br/><a NAME="E12:28_1"/><span class="lab"><font color="Green" title="E52">A24</font></span>: 
<font color="Maroon" title="c12">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:28"><span class="lab"><font color="Green" title="E41">A13</font></span></a>, <a class="txt" href="#E4:28_1"><span class="lab"><font color="Green" title="E46">A18</font></span></a>, <a class="txt" href="#E8:28_1"><span class="lab"><font color="Green" title="E49">A21</font></span></a>, <a class="txt" href="#E7:28_1"><span class="lab"><font color="Green" title="E48">A20</font></span></a>, <a class="ref" href="aff_1.html#T40" title="AFF_1:th.40">AFF_1:40</a>, <a class="ref" href="aff_1.html#T58" title="AFF_1:th.58">AFF_1:58</a></span>;<br/><a NAME="E13:28_1"/><span class="lab"><font color="Green" title="E53">A25</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:28_1"><span class="lab"><font color="Green" title="E50">A22</font></span></a>, <a class="txt" href="#E8:28_1"><span class="lab"><font color="Green" title="E49">A21</font></span></a>, <a class="txt" href="#E7:28_1"><span class="lab"><font color="Green" title="E48">A20</font></span></a>, <a class="txt" href="#E11:28_1"><span class="lab"><font color="Green" title="E51">A23</font></span></a>, <a class="ref" href="aff_1.html#T21" title="AFF_1:th.21">AFF_1:21</a></span>;<br/><a NAME="E14:28_1"/>
<font color="Maroon" title="c10">K</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a></span>;<br/><a NAME="E15:28_1"/><span class="kw">then </span>
<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="c4">x</font>,<font color="Maroon" title="c7">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E9:28"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="ref" href="aff_1.html#T31" title="AFF_1:th.31">AFF_1:31</a></span>;<br/><a NAME="E16:28_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E5:28"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="txt" href="#E6:28"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="#E5:28_1"><span class="lab"><font color="Green" title="E47">A19</font></span></a>, <a class="txt" href="#E12:28_1"><span class="lab"><font color="Green" title="E52">A24</font></span></a>, <a class="txt" href="#E13:28_1"><span class="lab"><font color="Green" title="E53">A25</font></span></a>, <a class="txt" href="#E3:28_1"><span class="lab"><font color="Green" title="E45">A17</font></span></a>, <a class="txt" href="#E2:28_1"><span class="lab"><font color="Green" title="E44">A16</font></span></a>, <a class="txt" href="homothet.html#E3"><span class="lab"><font color="Green" title="E3">Lm3</font></span></a>, <a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a></span>;<br/><a NAME="E17:28_1"/><span class="kw">then </span>
<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="c7">y</font>,<font color="Maroon" title="c9">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E9:28"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="txt" href="#E10:28"><span class="lab"><font color="Green" title="E38">A10</font></span></a>, <a class="txt" href="#E11:28"><span class="lab"><font color="Green" title="E39">A11</font></span></a>, <a class="txt" href="#E13:28"><span class="lab"><font color="Green" title="E41">A13</font></span></a>, <a class="txt" href="#E12:28_1"><span class="lab"><font color="Green" title="E52">A24</font></span></a>, <a class="txt" href="#E13:28_1"><span class="lab"><font color="Green" title="E53">A25</font></span></a>, <a class="txt" href="#E1:28_1"><span class="lab"><font color="Green" title="E43">A15</font></span></a>, <a class="txt" href="homothet.html#E2"><span class="lab"><font color="Green" title="E2">Lm2</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E18:28_1"/>
<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c7">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</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>
<div><span class="lab"><font color="Green" title="E43">A26</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2"><span class="kw">now </span></a><div class="add"><span class="kw">set </span><font color="Maroon" title="c11">M</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>);<br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:28_2"/><span class="lab"><font color="Green" title="E44">A27</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">x</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c10">K</font>
 <span class="kw">and </span><br/><a NAME="E2:28_2"/><span class="lab"><font color="Green" title="E45">A28</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E3:28_2"/><span class="lab"><font color="Green" title="E46">A29</font></span>: 
<font color="Maroon" title="c5">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">q</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="c8">q</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c7">y</font></span><br/><a NAME="E4:28_2"/><span class="lab"><font color="Green" title="E47">A30</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>) is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28_2"><span class="lab"><font color="Green" title="E45">A28</font></span></a>, <a class="ref" href="aff_1.html#D3" title="AFF_1:def.3">AFF_1:def 3</a></span>;<br/><a NAME="E5:28_2"/>
<font color="Maroon" title="c10">K</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a></span>;<br/><a NAME="E6:28_2"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E1:28_2"><span class="lab"><font color="Green" title="E44">A27</font></span></a>, <a class="ref" href="aff_1.html#T31" title="AFF_1:th.31">AFF_1:31</a></span>;<br/><a NAME="E7:28_2"/><span class="kw">then </span>
 <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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E8:28_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A31</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</a></span>;<br/><a NAME="E9:28_2"/><span class="lab"><font color="Green" title="E49">A32</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E10:28_2"/><span class="lab"><font color="Green" title="E50">A33</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E11:28_2"/><span class="lab"><font color="Green" title="E51">A34</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>) <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c10">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E2:28_2"><span class="lab"><font color="Green" title="E45">A28</font></span></a>, <a class="ref" href="aff_1.html#D5" title="AFF_1:def.5">AFF_1:def 5</a></span>;<br/><a NAME="E12:28_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">y</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:28"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="ref" href="aff_1.html#T43" title="AFF_1:th.43">AFF_1:43</a></span>;<br/><a NAME="E13:28_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28_2"><span class="lab"><font color="Green" title="E47">A30</font></span></a>, <a class="txt" href="#E8:28_2"><span class="lab"><font color="Green" title="E48">A31</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></span>;<br/><span class="kw">hence </span><a NAME="E14:28_2"/>
<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c7">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E5:28"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="txt" href="#E6:28"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="txt" href="#E8:28"><span class="lab"><font color="Green" title="E36">A8</font></span></a>, <a class="txt" href="#E10:28"><span class="lab"><font color="Green" title="E38">A10</font></span></a>, <a class="txt" href="#E11:28"><span class="lab"><font color="Green" title="E39">A11</font></span></a>, <a class="txt" href="#E12:28"><span class="lab"><font color="Green" title="E40">A12</font></span></a>, <a class="txt" href="#E2:28_2"><span class="lab"><font color="Green" title="E45">A28</font></span></a>, <a class="txt" href="#E3:28_2"><span class="lab"><font color="Green" title="E46">A29</font></span></a>, <a class="txt" href="#E10:28_2"><span class="lab"><font color="Green" title="E50">A33</font></span></a>, <a class="txt" href="#E9:28_2"><span class="lab"><font color="Green" title="E49">A32</font></span></a>, <a class="txt" href="#E11:28_2"><span class="lab"><font color="Green" title="E51">A34</font></span></a>, <a class="txt" href="#E8:28_2"><span class="lab"><font color="Green" title="E48">A31</font></span></a>, <a class="ref" href="homothet.html#T7" target="_self" title="HOMOTHET:th.7">Th7</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="E16:28"/><span class="lab"><font color="Green" title="E44">A35</font></span>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">y</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">set </span><font color="Maroon" title="c11">M</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">y</font>);<br/>
<a NAME="E1:28_3"/><span class="lab"><font color="Green" title="E45">A36</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">y</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:28_3"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</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">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">y</font></span><br/>

<a NAME="E3:28_3"/><span class="kw">then </span>
<font color="Maroon" title="c6">p9</font>,<font color="Maroon" title="c4">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p9</font>,<font color="Maroon" title="c7">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E5:28"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="txt" href="#E8:28"><span class="lab"><font color="Green" title="E36">A8</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/>
<a NAME="E4:28_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">p9</font>,<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E5:28_3"/><span class="kw">then </span>
 <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">y</font>,<font color="Maroon" title="c6">p9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E6:28_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A37</font></span>: 
<font color="Maroon" title="c6">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">y</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E7:28_3"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">y</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="E8:28_3"/><span class="kw">then </span>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">y</font>) <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c10">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:28"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="ref" href="aff_1.html#D5" title="AFF_1:def.5">AFF_1:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:28_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="txt" href="#E6:28"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="#E1:28_3"><span class="lab"><font color="Green" title="E45">A36</font></span></a>, <a class="txt" href="#E6:28_3"><span class="lab"><font color="Green" title="E46">A37</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_4"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:28_4"/><span class="lab"><font color="Green" title="E45">A38</font></span>: 
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q</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="c8">q</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c7">y</font></span><br/><a NAME="E2:28_4"/>
<font color="Maroon" title="c6">p9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q9</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_4_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:28_4_1"/>
<font color="Maroon" title="c6">p9</font>,<font color="Maroon" title="c4">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c4">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E5:28"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="txt" href="#E12:28"><span class="lab"><font color="Green" title="E40">A12</font></span></a>, <a class="txt" href="#E1:28_4"><span class="lab"><font color="Green" title="E45">A38</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/>
<a NAME="E2:28_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c6">p9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c9">q9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E3:28_4_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c6">p9</font>,<font color="Maroon" title="c9">q9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E4:28_4_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A39</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">p9</font>,<font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c4">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:28_4_1"/>
<font color="Maroon" title="c6">p9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">q9</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/>

<span class="kw">hence </span><a NAME="E6:28_4_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="txt" href="#E6:28"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="#E11:28"><span class="lab"><font color="Green" title="E39">A11</font></span></a>, <a class="txt" href="#E4:28_4_1"><span class="lab"><font color="Green" title="E46">A39</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a>, <a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</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="E3:28_4"/>
<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c7">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:28"><span class="lab"><font color="Green" title="E36">A8</font></span></a>, <a class="txt" href="#E1:28_4"><span class="lab"><font color="Green" title="E45">A38</font></span></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="E18:28"/>
<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">q9</font>,<font color="Maroon" title="c7">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:28"><span class="lab"><font color="Green" title="E40">A12</font></span></a>, <a class="txt" href="#E16:28"><span class="lab"><font color="Green" title="E44">A35</font></span></a>, <a class="txt" href="#E14:28"><span class="lab"><font color="Green" title="E42">A14</font></span></a>, <a class="txt" href="#E15:28"><span class="lab"><font color="Green" title="E43">A26</font></span></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>
