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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">q</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">a'</font>, <font color="Olive" title="b6">b'</font>, <font color="Olive" title="b7">c'</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="b8">A</font>, <font color="Olive" title="b9">P</font>, <font color="Olive" title="b10">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">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">A</font> &amp; <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">P</font> &amp; <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b10">C</font> &amp; not <font color="Olive" title="b8">A</font>,<font color="Olive" title="b9">P</font>,<font color="Olive" title="b10">C</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a>  &amp; <font color="Olive" title="b1">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">a</font> &amp; <font color="Olive" title="b1">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b1">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">c</font> &amp; <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">A</font> &amp; <font color="Olive" title="b5">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">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="b9">P</font> &amp; <font color="Olive" title="b6">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">P</font> &amp; <font color="Olive" title="b4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b10">C</font> &amp; <font color="Olive" title="b7">c'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b10">C</font> &amp; <font color="Olive" title="b8">A</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Olive" title="b9">P</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Olive" title="b10">C</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Olive" title="b8">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b9">P</font> &amp; <font color="Olive" title="b8">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b10">C</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">a'</font>,<font color="Olive" title="b6">b'</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">a'</font>,<font color="Olive" title="b7">c'</font> holds <br/><font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">b'</font>,<font color="Olive" title="b7">c'</font></span><br/><b>let </b><font color="Maroon" title="c2">q</font>, <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c6">a'</font>, <font color="Maroon" title="c7">b'</font>, <font color="Maroon" title="c8">c'</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:()"><i><font color="Red">::  thesis: </font></i></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="Maroon" title="c2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">P</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c3">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="c6">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="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="c7">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">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="c8">c'</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> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Olive" title="b2">P</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Olive" title="b3">C</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_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="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c7">b'</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c8">c'</font> holds <br/><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c8">c'</font></span><br/><b>let </b><font color="Maroon" title="c9">A</font>, <font color="Maroon" title="c10">P</font>, <font color="Maroon" title="c11">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">P</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">C</font> &amp; not <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c10">P</font>,<font color="Maroon" title="c11">C</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a>  &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A</font> &amp; <font color="Maroon" title="c6">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">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="c10">P</font> &amp; <font color="Maroon" title="c7">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">P</font> &amp; <font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">C</font> &amp; <font color="Maroon" title="c8">c'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">C</font> &amp; <font color="Maroon" title="c9">A</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c10">P</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c11">C</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c9">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">P</font> &amp; <font color="Maroon" title="c9">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">C</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c7">b'</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c8">c'</font> implies <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c8">c'</font> )</span><br/>





















<b>assume </b><b>that </b><br/><a NAME="E1:63"/><i><font color="Green" title="E52">A1</font></i>: 
( <font color="Maroon" title="c2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">P</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">C</font> )
 <b>and </b><br/><a NAME="E2:63"/><i><font color="Green" title="E53">A2</font></i>: 
not <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c10">P</font>,<font color="Maroon" title="c11">C</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a> 
 <b>and </b><br/><a NAME="E3:63"/><i><font color="Green" title="E54">A3</font></i>: 
( <font color="Maroon" title="c2">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">c</font> )
 <b>and </b><br/><a NAME="E4:63"/><i><font color="Green" title="E55">A4</font></i>: 
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A</font> &amp; <font color="Maroon" title="c6">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">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="c10">P</font> &amp; <font color="Maroon" title="c7">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">P</font> &amp; <font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">C</font> &amp; <font color="Maroon" title="c8">c'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">C</font> )
 <b>and </b><br/><a NAME="E5:63"/><i><font color="Green" title="E56">A5</font></i>: 
( <font color="Maroon" title="c9">A</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c10">P</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c11">C</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  )
 <b>and </b><br/><a NAME="E6:63"/><i><font color="Green" title="E57">A6</font></i>: 
( <font color="Maroon" title="c9">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">P</font> &amp; <font color="Maroon" title="c9">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">C</font> )
 <b>and </b><br/><a NAME="E7:63"/><i><font color="Green" title="E58">A7</font></i>: 
( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c7">b'</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c8">c'</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c8">c'</font></span><br/>

<b>consider </b><font color="Maroon" title="c12">X</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font><b> such that </b><br/><a NAME="E9:63"/><i><font color="Green" title="E59">A8</font></i>: 
( <font color="Maroon" title="c10">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">X</font> &amp; <font color="Maroon" title="c11">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">X</font> )
 <b>and </b><br/><a NAME="E10:63"/><i><font color="Green" title="E60">A9</font></i>: 
<font color="Maroon" title="c12">X</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a> 
 <b>by </b><i><a class="txt" href="aff_4.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="aff_4.html#E5:63"><i><font color="Green" title="E56">A5</font></i></a>, <a class="ref" href="aff_4.html#T38" target="_self" title="AFF_4:th.38">Th38</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c13">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font><b> such that </b><br/><a NAME="E12:63"/><i><font color="Green" title="E61">A10</font></i>: 
( <font color="Maroon" title="c9">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">Y</font> &amp; <font color="Maroon" title="c11">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">Y</font> )
 <b>and </b><br/><a NAME="E13:63"/><i><font color="Green" title="E62">A11</font></i>: 
<font color="Maroon" title="c13">Y</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a> 
 <b>by </b><i><a class="txt" href="aff_4.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="aff_4.html#E5:63"><i><font color="Green" title="E56">A5</font></i></a>, <a class="ref" href="aff_4.html#T38" target="_self" title="AFF_4:th.38">Th38</a></i>;<br/>
<a NAME="E14:63"/><i><font color="Green" title="E63">A12</font></i>: 
<font color="Maroon" title="c10">P</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">C</font>
 
<b>by </b><i><a class="txt" href="aff_4.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="aff_4.html#E2:63"><i><font color="Green" title="E53">A2</font></i></a>, <a class="txt" href="aff_4.html#E5:63"><i><font color="Green" title="E56">A5</font></i></a>, <a class="ref" href="aff_4.html#T47" target="_self" title="AFF_4:th.47">Th47</a></i>;<br/>
<a NAME="E15:63"/><b>then </b><i><font color="Green" title="E64">A13</font></i>: 
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c5">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font> )
 
<b>by </b><i><a class="txt" href="aff_4.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="aff_4.html#E3:63"><i><font color="Green" title="E54">A3</font></i></a>, <a class="txt" href="aff_4.html#E4:63"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="aff_4.html#E5:63"><i><font color="Green" title="E56">A5</font></i></a>, <a class="txt" href="aff_4.html#E6:63"><i><font color="Green" title="E57">A6</font></i></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></i>;<br/>
<div><i><font color="Green" title="E65">A14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_1"/><i><font color="Green" title="E66">A15</font></i>: 
<font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c8">c'</font></span><br/><a NAME="E2:63_1"/><b>then </b><i><font color="Green" title="E67">A16</font></i>: 
<font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="aff_4.html#E3:63"><i><font color="Green" title="E54">A3</font></i></a>, <a class="txt" href="aff_4.html#E4:63"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="aff_4.html#E5:63"><i><font color="Green" title="E56">A5</font></i></a>, <a class="txt" href="aff_4.html#E6:63"><i><font color="Green" title="E57">A6</font></i></a>, <a class="txt" href="aff_4.html#E7:63"><i><font color="Green" title="E58">A7</font></i></a>, <a class="ref" href="aff_4.html#T8" target="_self" title="AFF_4:th.8">Th8</a></i>;<br/><a NAME="E3:63_1"/>
<font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="aff_4.html#E3:63"><i><font color="Green" title="E54">A3</font></i></a>, <a class="txt" href="aff_4.html#E4:63"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="aff_4.html#E5:63"><i><font color="Green" title="E56">A5</font></i></a>, <a class="txt" href="aff_4.html#E6:63"><i><font color="Green" title="E57">A6</font></i></a>, <a class="txt" href="aff_4.html#E7:63"><i><font color="Green" title="E58">A7</font></i></a>, <a class="txt" href="aff_4.html#E1:63_1"><i><font color="Green" title="E66">A15</font></i></a>, <a class="ref" href="aff_4.html#T8" target="_self" title="AFF_4:th.8">Th8</a></i>;<br/><b>hence </b><a NAME="E4:63_1"/>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c8">c'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E2:63_1"><i><font color="Green" title="E67">A16</font></i></a>, <a class="ref" href="aff_1.html#T12" title="AFF_1:th.12">AFF_1:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_2"/><i><font color="Green" title="E66">A17</font></i>: 
<font color="Maroon" title="c2">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c8">c'</font></span><br/><a NAME="E2:63_2"/><b>then </b><i><font color="Green" title="E67">A18</font></i>: 
<font color="Maroon" title="c2">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="aff_4.html#E3:63"><i><font color="Green" title="E54">A3</font></i></a>, <a class="txt" href="aff_4.html#E4:63"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="aff_4.html#E5:63"><i><font color="Green" title="E56">A5</font></i></a>, <a class="txt" href="aff_4.html#E6:63"><i><font color="Green" title="E57">A6</font></i></a>, <a class="txt" href="aff_4.html#E7:63"><i><font color="Green" title="E58">A7</font></i></a>, <a class="ref" href="aff_4.html#T8" target="_self" title="AFF_4:th.8">Th8</a></i>;<br/><div><i><font color="Green" title="E68">A19</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_2_1"/><i><font color="Green" title="E69">A20</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c8">c'</font></span><br/><a NAME="E2:63_2_1"/><b>then </b><i><font color="Green" title="E70">A21</font></i>: 
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="aff_4.html#E3:63"><i><font color="Green" title="E54">A3</font></i></a>, <a class="txt" href="aff_4.html#E4:63"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="aff_4.html#E5:63"><i><font color="Green" title="E56">A5</font></i></a>, <a class="txt" href="aff_4.html#E6:63"><i><font color="Green" title="E57">A6</font></i></a>, <a class="txt" href="aff_4.html#E7:63"><i><font color="Green" title="E58">A7</font></i></a>, <a class="ref" href="aff_4.html#T9" target="_self" title="AFF_4:th.9">Th9</a></i>;<br/><a NAME="E3:63_2_1"/>
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="aff_4.html#E3:63"><i><font color="Green" title="E54">A3</font></i></a>, <a class="txt" href="aff_4.html#E4:63"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="aff_4.html#E5:63"><i><font color="Green" title="E56">A5</font></i></a>, <a class="txt" href="aff_4.html#E6:63"><i><font color="Green" title="E57">A6</font></i></a>, <a class="txt" href="aff_4.html#E7:63"><i><font color="Green" title="E58">A7</font></i></a>, <a class="txt" href="aff_4.html#E1:63_2_1"><i><font color="Green" title="E69">A20</font></i></a>, <a class="ref" href="aff_4.html#T9" target="_self" title="AFF_4:th.9">Th9</a></i>;<br/><b>hence </b><a NAME="E4:63_2_1"/>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c8">c'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E2:63_2_1"><i><font color="Green" title="E70">A21</font></i></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_2_2"/><i><font color="Green" title="E69">A22</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c8">c'</font></span><br/><b>assume </b><a NAME="E2:63_2_2"/><i><font color="Green" title="E70">A23</font></i>: 
not <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c8">c'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E3:63_2_2"/><i><font color="Green" title="E71">A24</font></i>: 
( <font color="Maroon" title="c6">a'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b'</font> &amp; <font color="Maroon" title="c6">a'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c'</font> &amp; <font color="Maroon" title="c8">c'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b'</font> )
 <b>by </b><i><a class="txt" href="aff_4.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="aff_4.html#E4:63"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="aff_4.html#E5:63"><i><font color="Green" title="E56">A5</font></i></a>, <a class="txt" href="aff_4.html#E6:63"><i><font color="Green" title="E57">A6</font></i></a>, <a class="txt" href="aff_4.html#E14:63"><i><font color="Green" title="E63">A12</font></i></a>, <a class="txt" href="aff_4.html#E1:63_2"><i><font color="Green" title="E66">A17</font></i></a>, <a class="txt" href="aff_4.html#E2:63_2"><i><font color="Green" title="E67">A18</font></i></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></i>;<br/><b>set </b><font color="Maroon" title="c14">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="c5">c</font>;<br/><b>set </b><font color="Maroon" title="c15">BC'</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c8">c'</font>;<br/><b>set </b><font color="Maroon" title="c16">AB</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>;<br/><b>set </b><font color="Maroon" title="c17">AB'</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c7">b'</font>;<br/><b>set </b><font color="Maroon" title="c18">AC</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font>;<br/><b>set </b><font color="Maroon" title="c19">AC'</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c8">c'</font>;<br/><a NAME="E4:63_2_2"/><i><font color="Green" title="E72">A25</font></i>: 
(  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp;  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c8">c'</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp;  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp;  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c8">c'</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp;  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp;  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c7">b'</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  )
 <b>by </b><i><a class="txt" href="aff_4.html#E15:63"><i><font color="Green" title="E64">A13</font></i></a>, <a class="txt" href="aff_4.html#E3:63_2_2"><i><font color="Green" title="E71">A24</font></i></a>, <a class="ref" href="aff_1.html#D3" title="AFF_1:def.3">AFF_1:def 3</a></i>;<br/><a NAME="E5:63_2_2"/><i><font color="Green" title="E73">A26</font></i>: 
( <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="c3">a</font>,<font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c3">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="c3">a</font>,<font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c3">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="c3">a</font>,<font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c5">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="c3">a</font>,<font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c6">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="c6">a'</font>,<font color="Maroon" title="c8">c'</font> &amp; <font color="Maroon" title="c8">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="c6">a'</font>,<font color="Maroon" title="c8">c'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a></i>;<br/><a NAME="E6:63_2_2"/><i><font color="Green" title="E74">A27</font></i>: 
( <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="c5">c</font> &amp; <font color="Maroon" title="c5">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="c5">c</font> &amp; <font color="Maroon" title="c7">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="c7">b'</font>,<font color="Maroon" title="c8">c'</font> &amp; <font color="Maroon" title="c8">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="c7">b'</font>,<font color="Maroon" title="c8">c'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a></i>;<br/><a NAME="E7:63_2_2"/><i><font color="Green" title="E75">A28</font></i>: 
(  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c7">b'</font> &amp;  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c8">c'</font> )
 <b>by </b><i><a class="txt" href="aff_4.html#E7:63"><i><font color="Green" title="E58">A7</font></i></a>, <a class="txt" href="aff_4.html#E15:63"><i><font color="Green" title="E64">A13</font></i></a>, <a class="txt" href="aff_4.html#E3:63_2_2"><i><font color="Green" title="E71">A24</font></i></a>, <a class="ref" href="aff_1.html#T51" title="AFF_1:th.51">AFF_1:51</a></i>;<br/><a NAME="E8:63_2_2"/><i><font color="Green" title="E76">A29</font></i>: 
(  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">X</font> &amp;  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c8">c'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">X</font> )
 <b>by </b><i><a class="txt" href="aff_4.html#E4:63"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="aff_4.html#E9:63"><i><font color="Green" title="E59">A8</font></i></a>, <a class="txt" href="aff_4.html#E10:63"><i><font color="Green" title="E60">A9</font></i></a>, <a class="txt" href="aff_4.html#E15:63"><i><font color="Green" title="E64">A13</font></i></a>, <a class="txt" href="aff_4.html#E3:63_2_2"><i><font color="Green" title="E71">A24</font></i></a>, <a class="ref" href="aff_4.html#T19" target="_self" title="AFF_4:th.19">Th19</a></i>;<br/><a NAME="E9:63_2_2"/><i><font color="Green" title="E77">A30</font></i>: 
(  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">Y</font> &amp;  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c8">c'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">Y</font> )
 <b>by </b><i><a class="txt" href="aff_4.html#E4:63"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="aff_4.html#E12:63"><i><font color="Green" title="E61">A10</font></i></a>, <a class="txt" href="aff_4.html#E13:63"><i><font color="Green" title="E62">A11</font></i></a>, <a class="txt" href="aff_4.html#E15:63"><i><font color="Green" title="E64">A13</font></i></a>, <a class="txt" href="aff_4.html#E3:63_2_2"><i><font color="Green" title="E71">A24</font></i></a>, <a class="ref" href="aff_4.html#T19" target="_self" title="AFF_4:th.19">Th19</a></i>;<br/><b>consider </b><font color="Maroon" title="c20">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><b> such that </b><br/><a NAME="E11:63_2_2"/><i><font color="Green" title="E78">A31</font></i>: 
( <font color="Maroon" title="c20">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="c5">c</font> &amp; <font color="Maroon" title="c20">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="c7">b'</font>,<font color="Maroon" title="c8">c'</font> )
 <b>by </b><i><a class="txt" href="aff_4.html#E10:63"><i><font color="Green" title="E60">A9</font></i></a>, <a class="txt" href="aff_4.html#E4:63_2_2"><i><font color="Green" title="E72">A25</font></i></a>, <a class="txt" href="aff_4.html#E8:63_2_2"><i><font color="Green" title="E76">A29</font></i></a>, <a class="ref" href="aff_4.html#T22" target="_self" title="AFF_4:th.22">Th22</a>, <a class="txt" href="aff_4.html#E2:63_2_2"><i><font color="Green" title="E70">A23</font></i></a>, <a class="txt" href="aff_4.html#E6:63_2_2"><i><font color="Green" title="E74">A27</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><b>set </b><font color="Maroon" title="c21">K</font> = <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>;<br/><a NAME="E12:63_2_2"/><i><font color="Green" title="E79">A32</font></i>: 
( <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c20">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> &amp;  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> &amp;  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c7">b'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2_2_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:63_2_2_1"/>
<font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a> 
 <b>by </b><i><a class="txt" href="aff_4.html#E4:63_2_2"><i><font color="Green" title="E72">A25</font></i></a>, <a class="ref" href="aff_4.html#T27" target="_self" title="AFF_4:th.27">Th27</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c20">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> &amp;  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> &amp;  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c7">b'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> )</span><br/>

<b>thus </b><a NAME="E2:63_2_2_1"/>
( <font color="Maroon" title="c20">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> &amp;  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> )
 <b>by </b><i><a class="txt" href="aff_4.html#E4:63_2_2"><i><font color="Green" title="E72">A25</font></i></a>, <a class="ref" href="aff_4.html#D3" target="_self" title="AFF_4:def.3">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c7">b'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span></span><br/>

<b>hence </b><a NAME="E3:63_2_2_1"/>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c7">b'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="aff_4.html#E7:63_2_2"><i><font color="Green" title="E75">A28</font></i></a>, <a class="ref" href="aff_1.html#T58" title="AFF_1:th.58">AFF_1:58</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E13:63_2_2"/><i><font color="Green" title="E80">A33</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c20">p</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c'</font>,<font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c20">p</font> )
 <b>by </b><i><a class="txt" href="aff_4.html#E4:63_2_2"><i><font color="Green" title="E72">A25</font></i></a>, <a class="txt" href="aff_4.html#E6:63_2_2"><i><font color="Green" title="E74">A27</font></i></a>, <a class="txt" href="aff_4.html#E11:63_2_2"><i><font color="Green" title="E78">A31</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><b>then consider </b><font color="Maroon" title="c22">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><b> such that </b><br/><a NAME="E15:63_2_2"/><i><font color="Green" title="E81">A34</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c22">x</font> &amp; <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">p</font>,<font color="Maroon" title="c22">x</font> )
 <b>by </b><i><a class="txt" href="aff_4.html#E15:63"><i><font color="Green" title="E64">A13</font></i></a>, <a class="ref" href="aff_4.html#T1" target="_self" title="AFF_4:th.1">Th1</a></i>;<br/><b>consider </b><font color="Maroon" title="c23">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><b> such that </b><br/><a NAME="E17:63_2_2"/><i><font color="Green" title="E82">A35</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c'</font>,<font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c23">y</font> &amp; <font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c6">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">p</font>,<font color="Maroon" title="c23">y</font> )
 <b>by </b><i><a class="txt" href="aff_4.html#E3:63_2_2"><i><font color="Green" title="E71">A24</font></i></a>, <a class="txt" href="aff_4.html#E13:63_2_2"><i><font color="Green" title="E80">A33</font></i></a>, <a class="ref" href="aff_4.html#T1" target="_self" title="AFF_4:th.1">Th1</a></i>;<br/><a NAME="E18:63_2_2"/><i><font color="Green" title="E83">A36</font></i>: 
( <font color="Maroon" title="c22">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> &amp; <font color="Maroon" title="c23">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:63_2_2_2"/>
<font color="Maroon" title="c20">p</font>,<font color="Maroon" title="c22">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 
<b>by </b><i><a class="txt" href="aff_4.html#E15:63_2_2"><i><font color="Green" title="E81">A34</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E2:63_2_2_2"/><b>then </b>
<font color="Maroon" title="c20">p</font>,<font color="Maroon" title="c22">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="c3">a</font>,<font color="Maroon" title="c4">b</font>
 
<b>by </b><i><a class="txt" href="aff_4.html#E15:63"><i><font color="Green" title="E64">A13</font></i></a>, <a class="ref" href="aff_1.html#D4" title="AFF_1:def.4">AFF_1:def 4</a></i>;<br/>
<a NAME="E3:63_2_2_2"/><b>then </b>
<font color="Maroon" title="c20">p</font>,<font color="Maroon" title="c22">x</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 
<b>by </b><i><a class="txt" href="aff_4.html#E12:63_2_2"><i><font color="Green" title="E79">A32</font></i></a>, <a class="ref" href="aff_4.html#T3" target="_self" title="AFF_4:th.3">Th3</a></i>;<br/>
<b>hence </b><a NAME="E4:63_2_2_2"/>
<font color="Maroon" title="c22">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="aff_4.html#E12:63_2_2"><i><font color="Green" title="E79">A32</font></i></a>, <a class="ref" href="aff_4.html#T2" target="_self" title="AFF_4:th.2">Th2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c23">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span></span><br/>

<a NAME="E5:63_2_2_2"/>
<font color="Maroon" title="c20">p</font>,<font color="Maroon" title="c23">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c7">b'</font>
 
<b>by </b><i><a class="txt" href="aff_4.html#E17:63_2_2"><i><font color="Green" title="E82">A35</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E6:63_2_2_2"/><b>then </b>
<font color="Maroon" title="c20">p</font>,<font color="Maroon" title="c23">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="c6">a'</font>,<font color="Maroon" title="c7">b'</font>
 
<b>by </b><i><a class="txt" href="aff_4.html#E3:63_2_2"><i><font color="Green" title="E71">A24</font></i></a>, <a class="ref" href="aff_1.html#D4" title="AFF_1:def.4">AFF_1:def 4</a></i>;<br/>
<a NAME="E7:63_2_2_2"/><b>then </b>
<font color="Maroon" title="c20">p</font>,<font color="Maroon" title="c23">y</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 
<b>by </b><i><a class="txt" href="aff_4.html#E12:63_2_2"><i><font color="Green" title="E79">A32</font></i></a>, <a class="ref" href="aff_4.html#T3" target="_self" title="AFF_4:th.3">Th3</a></i>;<br/>
<b>hence </b><a NAME="E8:63_2_2_2"/>
<font color="Maroon" title="c23">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">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="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="aff_4.html#E12:63_2_2"><i><font color="Green" title="E79">A32</font></i></a>, <a class="ref" href="aff_4.html#T2" target="_self" title="AFF_4:th.2">Th2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E19:63_2_2"/><i><font color="Green" title="E84">A37</font></i>: 
( <font color="Maroon" title="c22">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="c3">a</font>,<font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c23">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="c6">a'</font>,<font color="Maroon" title="c8">c'</font> )
 <b>by </b><i><a class="txt" href="aff_4.html#E15:63"><i><font color="Green" title="E64">A13</font></i></a>, <a class="txt" href="aff_4.html#E3:63_2_2"><i><font color="Green" title="E71">A24</font></i></a>, <a class="txt" href="aff_4.html#E4:63_2_2"><i><font color="Green" title="E72">A25</font></i></a>, <a class="txt" href="aff_4.html#E5:63_2_2"><i><font color="Green" title="E73">A26</font></i></a>, <a class="txt" href="aff_4.html#E15:63_2_2"><i><font color="Green" title="E81">A34</font></i></a>, <a class="txt" href="aff_4.html#E17:63_2_2"><i><font color="Green" title="E82">A35</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><div><i><font color="Green" title="E85">A38</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2_2_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_2_2_3"/>
<font color="Maroon" title="c22">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:63_2_2_3"/><b>then </b>
<font color="Maroon" title="c6">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="c3">a</font>,<font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E5:63_2_2"><i><font color="Green" title="E73">A26</font></i></a>, <a class="txt" href="aff_4.html#E7:63_2_2"><i><font color="Green" title="E75">A28</font></i></a>, <a class="txt" href="aff_4.html#E19:63_2_2"><i><font color="Green" title="E84">A37</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>;<br/><a NAME="E3:63_2_2_3"/><b>then </b>
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E4:63"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="aff_4.html#E5:63"><i><font color="Green" title="E56">A5</font></i></a>, <a class="txt" href="aff_4.html#E1:63_2_2"><i><font color="Green" title="E69">A22</font></i></a>, <a class="txt" href="aff_4.html#E4:63_2_2"><i><font color="Green" title="E72">A25</font></i></a>, <a class="txt" href="aff_4.html#E5:63_2_2"><i><font color="Green" title="E73">A26</font></i></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></i>;<br/><b>hence </b><a NAME="E4:63_2_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_4.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="aff_4.html#E3:63"><i><font color="Green" title="E54">A3</font></i></a>, <a class="txt" href="aff_4.html#E4:63"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="aff_4.html#E5:63"><i><font color="Green" title="E56">A5</font></i></a>, <a class="txt" href="aff_4.html#E6:63"><i><font color="Green" title="E57">A6</font></i></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2_2_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_2_2_4"/><i><font color="Green" title="E86">A39</font></i>: 
<font color="Maroon" title="c22">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:63_2_2_4"/><b>then </b>
<font color="Maroon" title="c20">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="c3">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="c22">x</font>,<font color="Maroon" title="c23">y</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E12:63_2_2"><i><font color="Green" title="E79">A32</font></i></a>, <a class="txt" href="aff_4.html#E18:63_2_2"><i><font color="Green" title="E83">A36</font></i></a>, <a class="ref" href="aff_1.html#T71" title="AFF_1:th.71">AFF_1:71</a></i>;<br/><a NAME="E3:63_2_2_4"/><b>then </b>
<font color="Maroon" title="c20">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="c3">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="c13">Y</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E13:63"><i><font color="Green" title="E62">A11</font></i></a>, <a class="txt" href="aff_4.html#E9:63_2_2"><i><font color="Green" title="E77">A30</font></i></a>, <a class="txt" href="aff_4.html#E19:63_2_2"><i><font color="Green" title="E84">A37</font></i></a>, <a class="txt" href="aff_4.html#E1:63_2_2_4"><i><font color="Green" title="E86">A39</font></i></a>, <a class="ref" href="aff_4.html#T19" target="_self" title="AFF_4:th.19">Th19</a></i>;<br/><a NAME="E4:63_2_2_4"/><b>then </b><i><font color="Green" title="E87">A40</font></i>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">Y</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E4:63"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="aff_4.html#E12:63"><i><font color="Green" title="E61">A10</font></i></a>, <a class="txt" href="aff_4.html#E13:63"><i><font color="Green" title="E62">A11</font></i></a>, <a class="txt" href="aff_4.html#E5:63_2_2"><i><font color="Green" title="E73">A26</font></i></a>, <a class="txt" href="aff_4.html#E12:63_2_2"><i><font color="Green" title="E79">A32</font></i></a>, <a class="ref" href="aff_4.html#T23" target="_self" title="AFF_4:th.23">Th23</a></i>;<br/><a NAME="E5:63_2_2_4"/>
<font color="Maroon" title="c10">P</font> <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="c2">q</font>,<font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="aff_4.html#E3:63"><i><font color="Green" title="E54">A3</font></i></a>, <a class="txt" href="aff_4.html#E4:63"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="aff_4.html#E5:63"><i><font color="Green" title="E56">A5</font></i></a>, <a class="ref" href="aff_1.html#T71" title="AFF_1:th.71">AFF_1:71</a></i>;<br/><a NAME="E6:63_2_2_4"/><b>then </b>
<font color="Maroon" title="c10">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">Y</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="aff_4.html#E3:63"><i><font color="Green" title="E54">A3</font></i></a>, <a class="txt" href="aff_4.html#E12:63"><i><font color="Green" title="E61">A10</font></i></a>, <a class="txt" href="aff_4.html#E13:63"><i><font color="Green" title="E62">A11</font></i></a>, <a class="txt" href="aff_4.html#E5:63_2_2"><i><font color="Green" title="E73">A26</font></i></a>, <a class="txt" href="aff_4.html#E4:63_2_2_4"><i><font color="Green" title="E87">A40</font></i></a>, <a class="ref" href="aff_4.html#T19" target="_self" title="AFF_4:th.19">Th19</a></i>;<br/><b>hence </b><a NAME="E7:63_2_2_4"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_4.html#E2:63"><i><font color="Green" title="E53">A2</font></i></a>, <a class="txt" href="aff_4.html#E12:63"><i><font color="Green" title="E61">A10</font></i></a>, <a class="txt" href="aff_4.html#E13:63"><i><font color="Green" title="E62">A11</font></i></a>, <a class="ref" href="aff_4.html#D5" target="_self" title="AFF_4:def.5">Def5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E22:63_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_4.html#E20:63_2_2"><i><font color="Green" title="E85">A38</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E5:63_2"/>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c8">c'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E3:63_2"><i><font color="Green" title="E68">A19</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E18:63"/>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b'</font>,<font color="Maroon" title="c8">c'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E16:63"><i><font color="Green" title="E65">A14</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
