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<span class="kw">let </span><font color="Maroon" title="c1">AS</font> be   <a href="diraf.html#NM1" title="DIRAF:NM.1">AffinSpace</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">a9</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">b9</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">c9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><br/>  for <font color="Olive" title="b7">A</font>, <font color="Olive" title="b8">P</font>, <font color="Olive" title="b9">C</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font>  st <font color="Olive" title="b7">A</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Olive" title="b8">P</font> &amp; <font color="Olive" title="b7">A</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Olive" title="b9">C</font> &amp;  not <font color="Olive" title="b7">A</font>,<font color="Olive" title="b8">P</font>,<font color="Olive" title="b9">C</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a>  &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b7">A</font> &amp; <font color="Olive" title="b2">a9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b7">A</font> &amp; <font color="Olive" title="b3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">P</font> &amp; <font color="Olive" title="b4">b9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">P</font> &amp; <font color="Olive" title="b5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">C</font> &amp; <font color="Olive" title="b6">c9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">C</font> &amp; <font color="Olive" title="b7">A</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Olive" title="b7">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b8">P</font> &amp; <font color="Olive" title="b7">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b9">C</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b4">b9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b6">c9</font> holds <br/><font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b6">c9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">a9</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">b9</font>, <font color="Maroon" title="c6">c</font>, <font color="Maroon" title="c7">c9</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</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">A</font>, <font color="Olive" title="b2">P</font>, <font color="Olive" title="b3">C</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font>  st <font color="Olive" title="b1">A</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Olive" title="b2">P</font> &amp; <font color="Olive" title="b1">A</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Olive" title="b3">C</font> &amp;  not <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">C</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A</font> &amp; <font color="Maroon" title="c3">a9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A</font> &amp; <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">P</font> &amp; <font color="Maroon" title="c5">b9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">P</font> &amp; <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">C</font> &amp; <font color="Maroon" title="c7">c9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">C</font> &amp; <font color="Olive" title="b1">A</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</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">P</font> &amp; <font color="Olive" title="b1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">C</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c7">c9</font> holds <br/><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c8">A</font>, <font color="Maroon" title="c9">P</font>, <font color="Maroon" title="c10">C</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</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">A</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c9">P</font> &amp; <font color="Maroon" title="c8">A</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c10">C</font> &amp;  not <font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c9">P</font>,<font color="Maroon" title="c10">C</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A</font> &amp; <font color="Maroon" title="c3">a9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A</font> &amp; <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">P</font> &amp; <font color="Maroon" title="c5">b9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">P</font> &amp; <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">C</font> &amp; <font color="Maroon" title="c7">c9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">C</font> &amp; <font color="Maroon" title="c8">A</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c8">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">P</font> &amp; <font color="Maroon" title="c8">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">C</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c7">c9</font> implies <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font> )</span><br/>



















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:65"/><span class="lab"><font color="Green" title="E54">A1</font></span>: 
<font color="Maroon" title="c8">A</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c9">P</font>
 <span class="kw">and </span><br/><a NAME="E2:65"/><span class="lab"><font color="Green" title="E55">A2</font></span>: 
<font color="Maroon" title="c8">A</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c10">C</font>
 <span class="kw">and </span><br/><a NAME="E3:65"/><span class="lab"><font color="Green" title="E56">A3</font></span>: 
 not <font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c9">P</font>,<font color="Maroon" title="c10">C</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a> 
 <span class="kw">and </span><br/><a NAME="E4:65"/><span class="lab"><font color="Green" title="E57">A4</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A</font>
 <span class="kw">and </span><br/><a NAME="E5:65"/><span class="lab"><font color="Green" title="E58">A5</font></span>: 
<font color="Maroon" title="c3">a9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A</font>
 <span class="kw">and </span><br/><a NAME="E6:65"/><span class="lab"><font color="Green" title="E59">A6</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">P</font>
 <span class="kw">and </span><br/><a NAME="E7:65"/><span class="lab"><font color="Green" title="E60">A7</font></span>: 
<font color="Maroon" title="c5">b9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">P</font>
 <span class="kw">and </span><br/><a NAME="E8:65"/><span class="lab"><font color="Green" title="E61">A8</font></span>: 
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">C</font>
 <span class="kw">and </span><br/><a NAME="E9:65"/><span class="lab"><font color="Green" title="E62">A9</font></span>: 
<font color="Maroon" title="c7">c9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">C</font>
 <span class="kw">and </span><br/><a NAME="E10:65"/><span class="lab"><font color="Green" title="E63">A10</font></span>: 
<font color="Maroon" title="c8">A</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E11:65"/><span class="lab"><font color="Green" title="E64">A11</font></span>: 
<font color="Maroon" title="c8">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">P</font>
 <span class="kw">and </span><br/><a NAME="E12:65"/><span class="lab"><font color="Green" title="E65">A12</font></span>: 
<font color="Maroon" title="c8">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">C</font>
 <span class="kw">and </span><br/><a NAME="E13:65"/><span class="lab"><font color="Green" title="E66">A13</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font>
 <span class="kw">and </span><br/><a NAME="E14:65"/><span class="lab"><font color="Green" title="E67">A14</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c7">c9</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="c6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font></span><br/>

<a NAME="E15:65"/><span class="lab"><font color="Green" title="E68">A15</font></span>: 
<font color="Maroon" title="c6">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65"><span class="lab"><font color="Green" title="E55">A2</font></span></a>, <a class="txt" href="#E4:65"><span class="lab"><font color="Green" title="E57">A4</font></span></a>, <a class="txt" href="#E8:65"><span class="lab"><font color="Green" title="E61">A8</font></span></a>, <a class="txt" href="#E12:65"><span class="lab"><font color="Green" title="E65">A12</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>;<br/>
<a NAME="E16:65"/><span class="lab"><font color="Green" title="E69">A16</font></span>: 
<font color="Maroon" title="c9">P</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c10">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="txt" href="#E2:65"><span class="lab"><font color="Green" title="E55">A2</font></span></a>, <a class="ref" href="aff_1.html#T44" title="AFF_1:th.44">AFF_1:44</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">X</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font><span class="kw"> such that </span><br/><a NAME="E18:65"/><span class="lab"><font color="Green" title="E70">A17</font></span>: 
( <font color="Maroon" title="c9">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">X</font> &amp; <font color="Maroon" title="c10">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">X</font> )
 <span class="kw">and </span><br/><a NAME="E19:65"/><span class="lab"><font color="Green" title="E71">A18</font></span>: 
<font color="Maroon" title="c11">X</font> is  <a href="aff_4.html#V1" title="AFF_4:attr.1">being_plane</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_4.html#T39" target="_self" title="AFF_4:th.39">Th39</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c12">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font><span class="kw"> such that </span><br/><a NAME="E21:65"/><span class="lab"><font color="Green" title="E72">A19</font></span>: 
<font color="Maroon" title="c8">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">and </span><br/><a NAME="E22:65"/><span class="lab"><font color="Green" title="E73">A20</font></span>: 
<font color="Maroon" title="c10">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">and </span><br/><a NAME="E23:65"/><span class="lab"><font color="Green" title="E74">A21</font></span>: 
<font color="Maroon" title="c12">Y</font> is  <a href="aff_4.html#V1" title="AFF_4:attr.1">being_plane</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65"><span class="lab"><font color="Green" title="E55">A2</font></span></a>, <a class="ref" href="aff_4.html#T39" target="_self" title="AFF_4:th.39">Th39</a></span>;<br/>
<a NAME="E24:65"/><span class="lab"><font color="Green" title="E75">A22</font></span>: 
<font color="Maroon" title="c9">P</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65"><span class="lab"><font color="Green" title="E56">A3</font></span></a>, <a class="txt" href="#E21:65"><span class="lab"><font color="Green" title="E72">A19</font></span></a>, <a class="txt" href="#E22:65"><span class="lab"><font color="Green" title="E73">A20</font></span></a>, <a class="txt" href="#E23:65"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="ref" href="aff_4.html#D5" target="_self" title="AFF_4:def.5">Def5</a></span>;<br/>
<a NAME="E25:65"/><span class="kw">then </span><span class="lab"><font color="Green" title="E76">A23</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:65"><span class="lab"><font color="Green" title="E59">A6</font></span></a>, <a class="txt" href="#E8:65"><span class="lab"><font color="Green" title="E61">A8</font></span></a>, <a class="txt" href="#E16:65"><span class="lab"><font color="Green" title="E69">A16</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>;<br/>
<a NAME="E26:65"/><span class="lab"><font color="Green" title="E77">A24</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="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="txt" href="#E4:65"><span class="lab"><font color="Green" title="E57">A4</font></span></a>, <a class="txt" href="#E6:65"><span class="lab"><font color="Green" title="E59">A6</font></span></a>, <a class="txt" href="#E11:65"><span class="lab"><font color="Green" title="E64">A11</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E78">A25</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1"><span class="kw">now </span></a><div class="add"><span class="kw">set </span><font color="Maroon" title="c13">BC</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font>);<br/><span class="kw">set </span><font color="Maroon" title="c14">BC9</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font>);<br/><span class="kw">set </span><font color="Maroon" title="c15">AB</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">b</font>);<br/><span class="kw">set </span><font color="Maroon" title="c16">AB9</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font>);<br/><span class="kw">set </span><font color="Maroon" title="c17">AC</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="c6">c</font>);<br/><span class="kw">set </span><font color="Maroon" title="c18">AC9</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c7">c9</font>);<br/><span class="kw">assume </span><a NAME="E1:65_1"/><span class="lab"><font color="Green" title="E79">A26</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">a9</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="c6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font></span><br/><span class="kw">assume </span><a NAME="E2:65_1"/><span class="lab"><font color="Green" title="E80">A27</font></span>: 
 not <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</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="E3:65_1"/><span class="lab"><font color="Green" title="E81">A28</font></span>: 
( <font color="Maroon" title="c5">b9</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="c5">b9</font>,<font color="Maroon" title="c7">c9</font>) &amp; <font color="Maroon" title="c7">c9</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="c5">b9</font>,<font color="Maroon" title="c7">c9</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="E4:65_1"/><span class="lab"><font color="Green" title="E82">A29</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:65"><span class="lab"><font color="Green" title="E59">A6</font></span></a>, <a class="txt" href="#E8:65"><span class="lab"><font color="Green" title="E61">A8</font></span></a>, <a class="txt" href="#E18:65"><span class="lab"><font color="Green" title="E70">A17</font></span></a>, <a class="txt" href="#E19:65"><span class="lab"><font color="Green" title="E71">A18</font></span></a>, <a class="txt" href="#E25:65"><span class="lab"><font color="Green" title="E76">A23</font></span></a>, <a class="ref" href="aff_4.html#T19" target="_self" title="AFF_4:th.19">Th19</a></span>;<br/><a NAME="E5:65_1"/><span class="lab"><font color="Green" title="E83">A30</font></span>: 
<font color="Maroon" title="c6">c</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">b</font>,<font color="Maroon" title="c6">c</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="E6:65_1"/><span class="lab"><font color="Green" title="E84">A31</font></span>: 
(  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font>) is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c4">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="c4">b</font>,<font color="Maroon" title="c6">c</font>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:65"><span class="lab"><font color="Green" title="E76">A23</font></span></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#D3" title="AFF_1:def.3">AFF_1:def 3</a></span>;<br/><a NAME="E7:65_1"/><span class="lab"><font color="Green" title="E85">A32</font></span>: 
<font color="Maroon" title="c7">c9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:65"><span class="lab"><font color="Green" title="E60">A7</font></span></a>, <a class="txt" href="#E9:65"><span class="lab"><font color="Green" title="E62">A9</font></span></a>, <a class="txt" href="#E16:65"><span class="lab"><font color="Green" title="E69">A16</font></span></a>, <a class="txt" href="#E24:65"><span class="lab"><font color="Green" title="E75">A22</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>;<br/><a NAME="E8:65_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E86">A33</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</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="E9:65_1"/>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:65"><span class="lab"><font color="Green" title="E60">A7</font></span></a>, <a class="txt" href="#E9:65"><span class="lab"><font color="Green" title="E62">A9</font></span></a>, <a class="txt" href="#E18:65"><span class="lab"><font color="Green" title="E70">A17</font></span></a>, <a class="txt" href="#E19:65"><span class="lab"><font color="Green" title="E71">A18</font></span></a>, <a class="txt" href="#E7:65_1"><span class="lab"><font color="Green" title="E85">A32</font></span></a>, <a class="ref" href="aff_4.html#T19" target="_self" title="AFF_4:th.19">Th19</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c19">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><span class="kw"> such that </span><br/><a NAME="E11:65_1"/><span class="lab"><font color="Green" title="E87">A34</font></span>: 
<font color="Maroon" title="c19">p</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">b</font>,<font color="Maroon" title="c6">c</font>)
 <span class="kw">and </span><br/><a NAME="E12:65_1"/><span class="lab"><font color="Green" title="E88">A35</font></span>: 
<font color="Maroon" title="c19">p</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="c5">b9</font>,<font color="Maroon" title="c7">c9</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:65"><span class="lab"><font color="Green" title="E71">A18</font></span></a>, <a class="txt" href="#E2:65_1"><span class="lab"><font color="Green" title="E80">A27</font></span></a>, <a class="txt" href="#E8:65_1"><span class="lab"><font color="Green" title="E86">A33</font></span></a>, <a class="txt" href="#E6:65_1"><span class="lab"><font color="Green" title="E84">A31</font></span></a>, <a class="txt" href="#E5:65_1"><span class="lab"><font color="Green" title="E83">A30</font></span></a>, <a class="txt" href="#E3:65_1"><span class="lab"><font color="Green" title="E81">A28</font></span></a>, <a class="txt" href="#E4:65_1"><span class="lab"><font color="Green" title="E82">A29</font></span></a>, <a class="ref" href="aff_4.html#T22" target="_self" title="AFF_4:th.22">Th22</a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E13:65_1"/><span class="lab"><font color="Green" title="E89">A36</font></span>: 
<font color="Maroon" title="c3">a9</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="c3">a9</font>,<font color="Maroon" title="c7">c9</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="E14:65_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">c9</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c19">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:65_1"><span class="lab"><font color="Green" title="E86">A33</font></span></a>, <a class="txt" href="#E3:65_1"><span class="lab"><font color="Green" title="E81">A28</font></span></a>, <a class="txt" href="#E12:65_1"><span class="lab"><font color="Green" title="E88">A35</font></span></a>, <a class="ref" href="aff_1.html#T21" title="AFF_1:th.21">AFF_1:21</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c20">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><span class="kw"> such that </span><br/><a NAME="E16:65_1"/><span class="lab"><font color="Green" title="E90">A37</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">c9</font>,<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c20">y</font>
 <span class="kw">and </span><br/><a NAME="E17:65_1"/><span class="lab"><font color="Green" title="E91">A38</font></span>: 
<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c3">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">p</font>,<font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:65_1"><span class="lab"><font color="Green" title="E85">A32</font></span></a>, <a class="ref" href="aff_4.html#T1" target="_self" title="AFF_4:th.1">Th1</a></span>;<br/><a NAME="E18:65_1"/><span class="lab"><font color="Green" title="E92">A39</font></span>: 
<font color="Maroon" title="c6">c</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="c6">c</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="E19:65_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c19">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:65_1"><span class="lab"><font color="Green" title="E84">A31</font></span></a>, <a class="txt" href="#E5:65_1"><span class="lab"><font color="Green" title="E83">A30</font></span></a>, <a class="txt" href="#E11:65_1"><span class="lab"><font color="Green" title="E87">A34</font></span></a>, <a class="ref" href="aff_1.html#T21" title="AFF_1:th.21">AFF_1:21</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c21">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><span class="kw"> such that </span><br/><a NAME="E21:65_1"/><span class="lab"><font color="Green" title="E93">A40</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c21">x</font>
 <span class="kw">and </span><br/><a NAME="E22:65_1"/><span class="lab"><font color="Green" title="E94">A41</font></span>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">p</font>,<font color="Maroon" title="c21">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:65"><span class="lab"><font color="Green" title="E76">A23</font></span></a>, <a class="ref" href="aff_4.html#T1" target="_self" title="AFF_4:th.1">Th1</a></span>;<br/><a NAME="E23:65_1"/><span class="lab"><font color="Green" title="E95">A42</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">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="E24:65_1"/><span class="lab"><font color="Green" title="E96">A43</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="c6">c</font>) is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <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="c6">c</font>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:65"><span class="lab"><font color="Green" title="E68">A15</font></span></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#D3" title="AFF_1:def.3">AFF_1:def 3</a></span>;<br/><a NAME="E25:65_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E97">A44</font></span>: 
<font color="Maroon" title="c21">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="c6">c</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:65"><span class="lab"><font color="Green" title="E68">A15</font></span></a>, <a class="txt" href="#E18:65_1"><span class="lab"><font color="Green" title="E92">A39</font></span></a>, <a class="txt" href="#E21:65_1"><span class="lab"><font color="Green" title="E93">A40</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c22">K</font> = <font color="Maroon" title="c19">p</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><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">b</font>)</span>)</span>;<br/><a NAME="E26:65_1"/><span class="lab"><font color="Green" title="E98">A45</font></span>: 
<font color="Maroon" title="c4">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="c4">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="E27:65_1"/><span class="lab"><font color="Green" title="E99">A46</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">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="#E26:65"><span class="lab"><font color="Green" title="E77">A24</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="E28:65_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E100">A47</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">b</font>) <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c19">p</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><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">b</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_4.html#D3" target="_self" title="AFF_4:def.3">Def3</a></span>;<br/><a NAME="E29:65_1"/><span class="lab"><font color="Green" title="E101">A48</font></span>: 
<font color="Maroon" title="c19">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">p</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><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">b</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:65_1"><span class="lab"><font color="Green" title="E99">A46</font></span></a>, <a class="ref" href="aff_4.html#D3" target="_self" title="AFF_4:def.3">Def3</a></span>;<br/><a NAME="E30:65_1"/>
<font color="Maroon" title="c19">p</font>,<font color="Maroon" title="c21">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:65_1"><span class="lab"><font color="Green" title="E94">A41</font></span></a>, <a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><a NAME="E31:65_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">p</font>,<font color="Maroon" title="c21">x</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="c4">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:65"><span class="lab"><font color="Green" title="E77">A24</font></span></a>, <a class="ref" href="aff_1.html#D4" title="AFF_1:def.4">AFF_1:def 4</a></span>;<br/><a NAME="E32:65_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">p</font>,<font color="Maroon" title="c21">x</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c19">p</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><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">b</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:65_1"><span class="lab"><font color="Green" title="E100">A47</font></span></a>, <a class="ref" href="aff_4.html#T3" target="_self" title="AFF_4:th.3">Th3</a></span>;<br/><a NAME="E33:65_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E102">A49</font></span>: 
<font color="Maroon" title="c21">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">p</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><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">b</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:65_1"><span class="lab"><font color="Green" title="E101">A48</font></span></a>, <a class="ref" href="aff_4.html#T2" target="_self" title="AFF_4:th.2">Th2</a></span>;<br/><a NAME="E34:65_1"/><span class="lab"><font color="Green" title="E103">A50</font></span>: 
<font color="Maroon" title="c3">a9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="txt" href="#E5:65"><span class="lab"><font color="Green" title="E58">A5</font></span></a>, <a class="txt" href="#E7:65"><span class="lab"><font color="Green" title="E60">A7</font></span></a>, <a class="txt" href="#E11:65"><span class="lab"><font color="Green" title="E64">A11</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>;<br/><a NAME="E35:65_1"/>
<font color="Maroon" title="c19">p</font>,<font color="Maroon" title="c20">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:65_1"><span class="lab"><font color="Green" title="E91">A38</font></span></a>, <a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><a NAME="E36:65_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E104">A51</font></span>: 
<font color="Maroon" title="c19">p</font>,<font color="Maroon" title="c20">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="c3">a9</font>,<font color="Maroon" title="c5">b9</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:65_1"><span class="lab"><font color="Green" title="E103">A50</font></span></a>, <a class="ref" href="aff_1.html#D4" title="AFF_1:def.4">AFF_1:def 4</a></span>;<br/><a NAME="E37:65_1"/>
 <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">b</font>) <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:65"><span class="lab"><font color="Green" title="E66">A13</font></span></a>, <a class="txt" href="#E26:65"><span class="lab"><font color="Green" title="E77">A24</font></span></a>, <a class="txt" href="#E34:65_1"><span class="lab"><font color="Green" title="E103">A50</font></span></a>, <a class="ref" href="aff_1.html#T37" title="AFF_1:th.37">AFF_1:37</a></span>;<br/><a NAME="E38:65_1"/><span class="kw">then </span>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font>) <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c19">p</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><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">b</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:65_1"><span class="lab"><font color="Green" title="E100">A47</font></span></a>, <a class="ref" href="aff_1.html#T44" title="AFF_1:th.44">AFF_1:44</a></span>;<br/><a NAME="E39:65_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">p</font>,<font color="Maroon" title="c20">y</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c19">p</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><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">b</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:65_1"><span class="lab"><font color="Green" title="E104">A51</font></span></a>, <a class="ref" href="aff_4.html#T3" target="_self" title="AFF_4:th.3">Th3</a></span>;<br/><a NAME="E40:65_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E105">A52</font></span>: 
<font color="Maroon" title="c20">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">p</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><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">b</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:65_1"><span class="lab"><font color="Green" title="E101">A48</font></span></a>, <a class="ref" href="aff_4.html#T2" target="_self" title="AFF_4:th.2">Th2</a></span>;<br/><a NAME="E41:65_1"/><span class="lab"><font color="Green" title="E106">A53</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="c6">c</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:65"><span class="lab"><font color="Green" title="E57">A4</font></span></a>, <a class="txt" href="#E8:65"><span class="lab"><font color="Green" title="E61">A8</font></span></a>, <a class="txt" href="#E21:65"><span class="lab"><font color="Green" title="E72">A19</font></span></a>, <a class="txt" href="#E22:65"><span class="lab"><font color="Green" title="E73">A20</font></span></a>, <a class="txt" href="#E23:65"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="txt" href="#E15:65"><span class="lab"><font color="Green" title="E68">A15</font></span></a>, <a class="ref" href="aff_4.html#T19" target="_self" title="AFF_4:th.19">Th19</a></span>;<br/><a NAME="E42:65_1"/><span class="lab"><font color="Green" title="E107">A54</font></span>: 
<font color="Maroon" title="c7">c9</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="c3">a9</font>,<font color="Maroon" title="c7">c9</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="E43:65_1"/><span class="lab"><font color="Green" title="E108">A55</font></span>: 
<font color="Maroon" title="c3">a9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65"><span class="lab"><font color="Green" title="E55">A2</font></span></a>, <a class="txt" href="#E5:65"><span class="lab"><font color="Green" title="E58">A5</font></span></a>, <a class="txt" href="#E9:65"><span class="lab"><font color="Green" title="E62">A9</font></span></a>, <a class="txt" href="#E12:65"><span class="lab"><font color="Green" title="E65">A12</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>;<br/><a NAME="E44:65_1"/><span class="kw">then </span>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c7">c9</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="E45:65_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E109">A56</font></span>: 
<font color="Maroon" title="c20">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="c3">a9</font>,<font color="Maroon" title="c7">c9</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:65_1"><span class="lab"><font color="Green" title="E108">A55</font></span></a>, <a class="txt" href="#E13:65_1"><span class="lab"><font color="Green" title="E89">A36</font></span></a>, <a class="txt" href="#E42:65_1"><span class="lab"><font color="Green" title="E107">A54</font></span></a>, <a class="txt" href="#E16:65_1"><span class="lab"><font color="Green" title="E90">A37</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/><a NAME="E46:65_1"/><span class="lab"><font color="Green" title="E110">A57</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c7">c9</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:65"><span class="lab"><font color="Green" title="E58">A5</font></span></a>, <a class="txt" href="#E9:65"><span class="lab"><font color="Green" title="E62">A9</font></span></a>, <a class="txt" href="#E21:65"><span class="lab"><font color="Green" title="E72">A19</font></span></a>, <a class="txt" href="#E22:65"><span class="lab"><font color="Green" title="E73">A20</font></span></a>, <a class="txt" href="#E23:65"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="txt" href="#E43:65_1"><span class="lab"><font color="Green" title="E108">A55</font></span></a>, <a class="ref" href="aff_4.html#T19" target="_self" title="AFF_4:th.19">Th19</a></span>;<br/><div><span class="lab"><font color="Green" title="E111">A58</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:65_1_1"/><span class="lab"><font color="Green" title="E112">A59</font></span>: 
<font color="Maroon" title="c21">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">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="E2:65_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">p</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><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">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c21">x</font>,<font color="Maroon" title="c20">y</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:65_1"><span class="lab"><font color="Green" title="E99">A46</font></span></a>, <a class="txt" href="#E33:65_1"><span class="lab"><font color="Green" title="E102">A49</font></span></a>, <a class="txt" href="#E40:65_1"><span class="lab"><font color="Green" title="E105">A52</font></span></a>, <a class="ref" href="aff_4.html#T27" target="_self" title="AFF_4:th.27">Th27</a>, <a class="ref" href="aff_1.html#T57" title="AFF_1:th.57">AFF_1:57</a></span>;<br/><a NAME="E3:65_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">p</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><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">b</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:65"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="txt" href="#E41:65_1"><span class="lab"><font color="Green" title="E106">A53</font></span></a>, <a class="txt" href="#E46:65_1"><span class="lab"><font color="Green" title="E110">A57</font></span></a>, <a class="txt" href="#E25:65_1"><span class="lab"><font color="Green" title="E97">A44</font></span></a>, <a class="txt" href="#E45:65_1"><span class="lab"><font color="Green" title="E109">A56</font></span></a>, <a class="txt" href="#E1:65_1_1"><span class="lab"><font color="Green" title="E112">A59</font></span></a>, <a class="ref" href="aff_4.html#T19" target="_self" title="AFF_4:th.19">Th19</a></span>;<br/><a NAME="E4:65_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E113">A60</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">b</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:65"><span class="lab"><font color="Green" title="E57">A4</font></span></a>, <a class="txt" href="#E21:65"><span class="lab"><font color="Green" title="E72">A19</font></span></a>, <a class="txt" href="#E23:65"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="txt" href="#E23:65_1"><span class="lab"><font color="Green" title="E95">A42</font></span></a>, <a class="txt" href="#E28:65_1"><span class="lab"><font color="Green" title="E100">A47</font></span></a>, <a class="ref" href="aff_4.html#T23" target="_self" title="AFF_4:th.23">Th23</a></span>;<br/><a NAME="E5:65_1_1"/>
<font color="Maroon" title="c9">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="txt" href="#E6:65"><span class="lab"><font color="Green" title="E59">A6</font></span></a>, <a class="txt" href="#E10:65"><span class="lab"><font color="Green" title="E63">A10</font></span></a>, <a class="ref" href="aff_4.html#D3" target="_self" title="AFF_4:def.3">Def3</a></span>;<br/><a NAME="E6:65_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:65"><span class="lab"><font color="Green" title="E63">A10</font></span></a>, <a class="txt" href="#E21:65"><span class="lab"><font color="Green" title="E72">A19</font></span></a>, <a class="txt" href="#E23:65"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="txt" href="#E26:65_1"><span class="lab"><font color="Green" title="E98">A45</font></span></a>, <a class="txt" href="#E4:65_1_1"><span class="lab"><font color="Green" title="E113">A60</font></span></a>, <a class="ref" href="aff_4.html#T28" target="_self" title="AFF_4:th.28">Th28</a></span>;<br/><span class="kw">hence </span><a NAME="E7:65_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65"><span class="lab"><font color="Green" title="E56">A3</font></span></a>, <a class="txt" href="#E21:65"><span class="lab"><font color="Green" title="E72">A19</font></span></a>, <a class="txt" href="#E22:65"><span class="lab"><font color="Green" title="E73">A20</font></span></a>, <a class="txt" href="#E23:65"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="ref" href="aff_4.html#D5" target="_self" title="AFF_4:def.5">Def5</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="E48:65_1"/><span class="lab"><font color="Green" title="E112">A61</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="c6">c</font>) <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c7">c9</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:65"><span class="lab"><font color="Green" title="E67">A14</font></span></a>, <a class="txt" href="#E15:65"><span class="lab"><font color="Green" title="E68">A15</font></span></a>, <a class="txt" href="#E43:65_1"><span class="lab"><font color="Green" title="E108">A55</font></span></a>, <a class="ref" href="aff_1.html#T37" title="AFF_1:th.37">AFF_1:37</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:65_1_2"/>
<font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">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="E2:65_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">a9</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="c6">c</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:65_1"><span class="lab"><font color="Green" title="E89">A36</font></span></a>, <a class="txt" href="#E48:65_1"><span class="lab"><font color="Green" title="E112">A61</font></span></a>, <a class="txt" href="#E25:65_1"><span class="lab"><font color="Green" title="E97">A44</font></span></a>, <a class="txt" href="#E45:65_1"><span class="lab"><font color="Green" title="E109">A56</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>;<br/><a NAME="E3:65_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:65"><span class="lab"><font color="Green" title="E57">A4</font></span></a>, <a class="txt" href="#E5:65"><span class="lab"><font color="Green" title="E58">A5</font></span></a>, <a class="txt" href="#E10:65"><span class="lab"><font color="Green" title="E63">A10</font></span></a>, <a class="txt" href="#E1:65_1"><span class="lab"><font color="Green" title="E79">A26</font></span></a>, <a class="txt" href="#E24:65_1"><span class="lab"><font color="Green" title="E96">A43</font></span></a>, <a class="txt" href="#E18:65_1"><span class="lab"><font color="Green" title="E92">A39</font></span></a>, <a class="ref" href="aff_1.html#T18" title="AFF_1:th.18">AFF_1:18</a></span>;<br/><span class="kw">hence </span><a NAME="E4:65_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65"><span class="lab"><font color="Green" title="E55">A2</font></span></a>, <a class="txt" href="#E8:65"><span class="lab"><font color="Green" title="E61">A8</font></span></a>, <a class="txt" href="#E12:65"><span class="lab"><font color="Green" title="E65">A12</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><span class="kw">hence </span><a NAME="E50:65_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E47:65_1"><span class="lab"><font color="Green" title="E111">A58</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>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:65_2"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a9</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="c6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font></span><br/><a NAME="E2:65_2"/><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">b9</font> &amp; <font color="Maroon" title="c6">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="txt" href="#E2:65"><span class="lab"><font color="Green" title="E55">A2</font></span></a>, <a class="txt" href="#E4:65"><span class="lab"><font color="Green" title="E57">A4</font></span></a>, <a class="txt" href="#E6:65"><span class="lab"><font color="Green" title="E59">A6</font></span></a>, <a class="txt" href="#E7:65"><span class="lab"><font color="Green" title="E60">A7</font></span></a>, <a class="txt" href="#E8:65"><span class="lab"><font color="Green" title="E61">A8</font></span></a>, <a class="txt" href="#E9:65"><span class="lab"><font color="Green" title="E62">A9</font></span></a>, <a class="txt" href="#E11:65"><span class="lab"><font color="Green" title="E64">A11</font></span></a>, <a class="txt" href="#E12:65"><span class="lab"><font color="Green" title="E65">A12</font></span></a>, <a class="txt" href="#E13:65"><span class="lab"><font color="Green" title="E66">A13</font></span></a>, <a class="txt" href="#E14:65"><span class="lab"><font color="Green" title="E67">A14</font></span></a>, <a class="ref" href="aff_4.html#T10" target="_self" title="AFF_4:th.10">Th10</a></span>;<br/><span class="kw">hence </span><a NAME="E3:65_2"/>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</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="E29:65"/>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:65"><span class="lab"><font color="Green" title="E78">A25</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>
