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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">a</font>, <font color="Olive" title="b2">a'</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">b'</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">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="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="Maroon" title="c1">AS</font> is  not   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a> &amp; <font color="Olive" title="b7">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Olive" title="b8">P</font> &amp; <font color="Olive" title="b7">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Olive" title="b9">C</font> &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">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="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">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="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">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="b7">A</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Olive" title="b8">P</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Olive" title="b9">C</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_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">a'</font>,<font color="Olive" title="b4">b'</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">a'</font>,<font color="Olive" title="b6">c'</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">b'</font>,<font color="Olive" title="b6">c'</font></span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">a'</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">b'</font>, <font color="Maroon" title="c6">c</font>, <font color="Maroon" title="c7">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="c1">AS</font> is  not   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a> &amp; <font color="Olive" title="b1">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Olive" title="b2">P</font> &amp; <font color="Olive" title="b1">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Olive" title="b3">C</font> &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">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="c5">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="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">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="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">a'</font>,<font color="Maroon" title="c5">b'</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">a'</font>,<font color="Maroon" title="c7">c'</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">b'</font>,<font color="Maroon" title="c7">c'</font></span><br/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">AS</font> is  not   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a> &amp; <font color="Maroon" title="c8">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c9">P</font> &amp; <font color="Maroon" title="c8">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c10">C</font> &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">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="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">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="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">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="c8">A</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c9">P</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c10">C</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_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">a'</font>,<font color="Maroon" title="c5">b'</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">a'</font>,<font color="Maroon" title="c7">c'</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">b'</font>,<font color="Maroon" title="c7">c'</font> )</span><br/>



















<b>assume </b><b>that </b><br/><a NAME="E1:67"/><i><font color="Green" title="E55">A1</font></i>: 
<font color="Maroon" title="c1">AS</font> is  not   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a>
 <b>and </b><br/><a NAME="E2:67"/><i><font color="Green" title="E56">A2</font></i>: 
( <font color="Maroon" title="c8">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c9">P</font> &amp; <font color="Maroon" title="c8">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c10">C</font> )
 <b>and </b><br/><a NAME="E3:67"/><i><font color="Green" title="E57">A3</font></i>: 
( <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">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="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">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="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">c'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">C</font> )
 <b>and </b><br/><a NAME="E4:67"/><i><font color="Green" title="E58">A4</font></i>: 
( <font color="Maroon" title="c8">A</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c9">P</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c10">C</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  )
 <b>and </b><br/><a NAME="E5:67"/><i><font color="Green" title="E59">A5</font></i>: 
( <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> )
 <b>and </b><br/><a NAME="E6:67"/><i><font color="Green" title="E60">A6</font></i>: 
( <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">a'</font>,<font color="Maroon" title="c5">b'</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">a'</font>,<font color="Maroon" title="c7">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="c6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c7">c'</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_1"/>
<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> 
 ; <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="c6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c7">c'</font></span><br/><b>then consider </b><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><b> such that </b><br/><a NAME="E3:67_1"/><i><font color="Green" title="E61">A7</font></i>: 
( <font color="Maroon" title="c8">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">X</font> &amp; <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> )
 <b>and </b><br/><a NAME="E4:67_1"/><i><font color="Green" title="E62">A8</font></i>: 
<font color="Maroon" title="c11">X</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a> 
 <b>by </b><i><a class="ref" href="aff_4.html#D5" target="_self" title="AFF_4:def.5">Def5</a></i>;<br/><b>consider </b><font color="Maroon" title="c12">d</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="E6:67_1"/><i><font color="Green" title="E63">A9</font></i>: 
not <font color="Maroon" title="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">X</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:67"><i><font color="Green" title="E55">A1</font></i></a>, <a class="txt" href="aff_4.html#E4:67_1"><i><font color="Green" title="E62">A8</font></i></a>, <a class="ref" href="aff_4.html#T48" target="_self" title="AFF_4:th.48">Th48</a></i>;<br/><b>set </b><font color="Maroon" title="c13">K</font> = <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font>;<br/><a NAME="E7:67_1"/><i><font color="Green" title="E64">A10</font></i>: 
( <font color="Maroon" title="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font> &amp; <font color="Maroon" title="c8">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font> )
 <b>by </b><i><a class="txt" href="aff_4.html#E4:67"><i><font color="Green" title="E58">A4</font></i></a>, <a class="ref" href="aff_4.html#D3" target="_self" title="AFF_4:def.3">Def3</a></i>;<br/><a NAME="E8:67_1"/><b>then </b><i><font color="Green" title="E65">A11</font></i>: 
( <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c9">P</font> &amp; <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c10">C</font> )
 <b>by </b><i><a class="txt" href="aff_4.html#E2:67"><i><font color="Green" title="E56">A2</font></i></a>, <a class="ref" href="aff_1.html#T58" title="AFF_1:th.58">AFF_1:58</a></i>;<br/><a NAME="E9:67_1"/><i><font color="Green" title="E66">A12</font></i>: 
<font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</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#E4:67"><i><font color="Green" title="E58">A4</font></i></a>, <a class="ref" href="aff_4.html#T27" target="_self" title="AFF_4:th.27">Th27</a></i>;<br/><a NAME="E10:67_1"/><i><font color="Green" title="E67">A13</font></i>: 
not <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">X</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E6:67_1"><i><font color="Green" title="E63">A9</font></i></a>, <a class="txt" href="aff_4.html#E7:67_1"><i><font color="Green" title="E64">A10</font></i></a></i>;<br/><a NAME="E11:67_1"/>
 ex <font color="Olive" title="b1">d'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b1">d'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a'</font>,<font color="Olive" title="b1">d'</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_1"><b>proof </b></a><div class="add">

<div><i><font color="Green" title="E68">A14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_1_1_1"/><i><font color="Green" title="E69">A15</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">d'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b1">d'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a'</font>,<font color="Olive" title="b1">d'</font> )</span><br/><b>consider </b><font color="Maroon" title="c14">d'</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="E3:67_1_1_1"/><i><font color="Green" title="E70">A16</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">d'</font>
 <b>and </b><br/><a NAME="E4:67_1_1_1"/><i><font color="Green" title="E71">A17</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a'</font>,<font color="Maroon" title="c14">d'</font>
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E5:67_1_1_1"/>
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">d'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">a'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E3:67_1_1_1"><i><font color="Green" title="E70">A16</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E6:67_1_1_1"/><b>then </b>
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">d'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c8">A</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E3:67"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="aff_4.html#E4:67"><i><font color="Green" title="E58">A4</font></i></a>, <a class="txt" href="aff_4.html#E1:67_1_1_1"><i><font color="Green" title="E69">A15</font></i></a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></i>;<br/><a NAME="E7:67_1_1_1"/><b>then </b>
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">d'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E7:67_1"><i><font color="Green" title="E64">A10</font></i></a>, <a class="ref" href="aff_4.html#T3" target="_self" title="AFF_4:th.3">Th3</a></i>;<br/><a NAME="E8:67_1_1_1"/><b>then </b>
<font color="Maroon" title="c14">d'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E7:67_1"><i><font color="Green" title="E64">A10</font></i></a>, <a class="ref" href="aff_4.html#T2" target="_self" title="AFF_4:th.2">Th2</a></i>;<br/><b>hence </b><a NAME="E9:67_1_1_1"/>
 ex <font color="Olive" title="b1">d'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b1">d'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a'</font>,<font color="Olive" title="b1">d'</font> )
 <b>by </b><i><a class="txt" href="aff_4.html#E4:67_1_1_1"><i><font color="Green" title="E71">A17</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>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_1_1_2"/><i><font color="Green" title="E69">A18</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">d'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b1">d'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a'</font>,<font color="Olive" title="b1">d'</font> )</span><br/><b>take </b><font color="Maroon" title="c14">d'</font> = <font color="Maroon" title="c12">d</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c14">d'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a'</font>,<font color="Maroon" title="c14">d'</font> )</span><br/><b>thus </b><a NAME="E2:67_1_1_2"/>
<font color="Maroon" title="c14">d'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E4:67"><i><font color="Green" title="E58">A4</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"> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a'</font>,<font color="Maroon" title="c14">d'</font></span><br/><b>thus </b><a NAME="E3:67_1_1_2"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a'</font>,<font color="Maroon" title="c14">d'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:67_1_1_2"><i><font color="Green" title="E69">A18</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>
<b>hence </b><a NAME="E3:67_1_1"/>
 ex <font color="Olive" title="b1">d'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b1">d'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a'</font>,<font color="Olive" title="b1">d'</font> )
 <b>by </b><i><a class="txt" href="aff_4.html#E1:67_1_1"><i><font color="Green" title="E68">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><b>end;</b></div><b>then consider </b><font color="Maroon" title="c14">d'</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="E13:67_1"/><i><font color="Green" title="E68">A19</font></i>: 
<font color="Maroon" title="c14">d'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font>
 <b>and </b><br/><a NAME="E14:67_1"/><i><font color="Green" title="E69">A20</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a'</font>,<font color="Maroon" title="c14">d'</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_1_2"/><i><font color="Green" title="E70">A21</font></i>: 
<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>
 ; <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="c6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c7">c'</font></span><br/><a NAME="E2:67_1_2"/><i><font color="Green" title="E71">A22</font></i>: 
<font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">A</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E3:67_1"><i><font color="Green" title="E61">A7</font></i></a>, <a class="txt" href="aff_4.html#E6:67_1"><i><font color="Green" title="E63">A9</font></i></a>, <a class="txt" href="aff_4.html#E7:67_1"><i><font color="Green" title="E64">A10</font></i></a></i>;<br/><a NAME="E3:67_1_2"/><i><font color="Green" title="E72">A23</font></i>: 
<font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <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>
 <b>by </b><i><a class="txt" href="aff_4.html#E3:67_1"><i><font color="Green" title="E61">A7</font></i></a>, <a class="txt" href="aff_4.html#E6:67_1"><i><font color="Green" title="E63">A9</font></i></a>, <a class="txt" href="aff_4.html#E7:67_1"><i><font color="Green" title="E64">A10</font></i></a></i>;<br/><a NAME="E4:67_1_2"/><i><font color="Green" title="E73">A24</font></i>: 
<font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <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>
 <b>by </b><i><a class="txt" href="aff_4.html#E3:67_1"><i><font color="Green" title="E61">A7</font></i></a>, <a class="txt" href="aff_4.html#E6:67_1"><i><font color="Green" title="E63">A9</font></i></a>, <a class="txt" href="aff_4.html#E7:67_1"><i><font color="Green" title="E64">A10</font></i></a></i>;<br/><a NAME="E5:67_1_2"/><i><font color="Green" title="E74">A25</font></i>: 
not <font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c10">C</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:67_1_2_1"/>
<font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c10">C</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:67_1_2_1"/><b>then </b>
<font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c10">C</font>,<font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a> 
 
<b>by </b><i><a class="ref" href="aff_4.html#T44" target="_self" title="AFF_4:th.44">Th44</a></i>;<br/>
<b>hence </b><a NAME="E3:67_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_4.html#E4:67"><i><font color="Green" title="E58">A4</font></i></a>, <a class="txt" href="aff_4.html#E5:67"><i><font color="Green" title="E59">A5</font></i></a>, <a class="txt" href="aff_4.html#E3:67_1"><i><font color="Green" title="E61">A7</font></i></a>, <a class="txt" href="aff_4.html#E4:67_1"><i><font color="Green" title="E62">A8</font></i></a>, <a class="txt" href="aff_4.html#E10:67_1"><i><font color="Green" title="E67">A13</font></i></a>, <a class="ref" href="aff_4.html#T46" target="_self" title="AFF_4:th.46">Th46</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="E6:67_1_2"/><i><font color="Green" title="E75">A26</font></i>: 
not <font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c9">P</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:67_1_2_2"/>
<font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c9">P</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:67_1_2_2"/><b>then </b>
<font color="Maroon" title="c8">A</font>,<font color="Maroon" title="c9">P</font>,<font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a> 
 
<b>by </b><i><a class="ref" href="aff_4.html#T44" target="_self" title="AFF_4:th.44">Th44</a></i>;<br/>
<b>hence </b><a NAME="E3:67_1_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_4.html#E4:67"><i><font color="Green" title="E58">A4</font></i></a>, <a class="txt" href="aff_4.html#E5:67"><i><font color="Green" title="E59">A5</font></i></a>, <a class="txt" href="aff_4.html#E3:67_1"><i><font color="Green" title="E61">A7</font></i></a>, <a class="txt" href="aff_4.html#E4:67_1"><i><font color="Green" title="E62">A8</font></i></a>, <a class="txt" href="aff_4.html#E10:67_1"><i><font color="Green" title="E67">A13</font></i></a>, <a class="ref" href="aff_4.html#T46" target="_self" title="AFF_4:th.46">Th46</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="E7:67_1_2"/><i><font color="Green" title="E76">A27</font></i>: 
not <font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <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> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:67_1_2_3"/>
<font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:67_1_2_3"/><b>then </b>
<font color="Maroon" title="c9">P</font>,<font color="Maroon" title="c10">C</font>,<font color="Maroon" title="c12">d</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c8">A</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a> 
 
<b>by </b><i><a class="ref" href="aff_4.html#T44" target="_self" title="AFF_4:th.44">Th44</a></i>;<br/>
<b>hence </b><a NAME="E3:67_1_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_4.html#E4:67"><i><font color="Green" title="E58">A4</font></i></a>, <a class="txt" href="aff_4.html#E3:67_1"><i><font color="Green" title="E61">A7</font></i></a>, <a class="txt" href="aff_4.html#E4:67_1"><i><font color="Green" title="E62">A8</font></i></a>, <a class="txt" href="aff_4.html#E10:67_1"><i><font color="Green" title="E67">A13</font></i></a>, <a class="txt" href="aff_4.html#E1:67_1_2"><i><font color="Green" title="E70">A21</font></i></a>, <a class="ref" href="aff_4.html#T46" target="_self" title="AFF_4:th.46">Th46</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="E8:67_1_2"/><i><font color="Green" title="E77">A28</font></i>: 
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d'</font>,<font color="Maroon" title="c7">c'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E2:67"><i><font color="Green" title="E56">A2</font></i></a>, <a class="txt" href="aff_4.html#E3:67"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="aff_4.html#E4:67"><i><font color="Green" title="E58">A4</font></i></a>, <a class="txt" href="aff_4.html#E5:67"><i><font color="Green" title="E59">A5</font></i></a>, <a class="txt" href="aff_4.html#E6:67"><i><font color="Green" title="E60">A6</font></i></a>, <a class="txt" href="aff_4.html#E7:67_1"><i><font color="Green" title="E64">A10</font></i></a>, <a class="txt" href="aff_4.html#E9:67_1"><i><font color="Green" title="E66">A12</font></i></a>, <a class="txt" href="aff_4.html#E13:67_1"><i><font color="Green" title="E68">A19</font></i></a>, <a class="txt" href="aff_4.html#E14:67_1"><i><font color="Green" title="E69">A20</font></i></a>, <a class="txt" href="aff_4.html#E2:67_1_2"><i><font color="Green" title="E71">A22</font></i></a>, <a class="txt" href="aff_4.html#E5:67_1_2"><i><font color="Green" title="E74">A25</font></i></a>, <a class="txt" href="aff_4.html#E66"><i><font color="Green" title="E53">Lm11</font></i></a></i>;<br/><a NAME="E9:67_1_2"/>
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d'</font>,<font color="Maroon" title="c5">b'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E2:67"><i><font color="Green" title="E56">A2</font></i></a>, <a class="txt" href="aff_4.html#E3:67"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="aff_4.html#E4:67"><i><font color="Green" title="E58">A4</font></i></a>, <a class="txt" href="aff_4.html#E5:67"><i><font color="Green" title="E59">A5</font></i></a>, <a class="txt" href="aff_4.html#E6:67"><i><font color="Green" title="E60">A6</font></i></a>, <a class="txt" href="aff_4.html#E7:67_1"><i><font color="Green" title="E64">A10</font></i></a>, <a class="txt" href="aff_4.html#E9:67_1"><i><font color="Green" title="E66">A12</font></i></a>, <a class="txt" href="aff_4.html#E13:67_1"><i><font color="Green" title="E68">A19</font></i></a>, <a class="txt" href="aff_4.html#E14:67_1"><i><font color="Green" title="E69">A20</font></i></a>, <a class="txt" href="aff_4.html#E2:67_1_2"><i><font color="Green" title="E71">A22</font></i></a>, <a class="txt" href="aff_4.html#E6:67_1_2"><i><font color="Green" title="E75">A26</font></i></a>, <a class="txt" href="aff_4.html#E66"><i><font color="Green" title="E53">Lm11</font></i></a></i>;<br/><b>hence </b><a NAME="E10:67_1_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">b'</font>,<font color="Maroon" title="c7">c'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E3:67"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="aff_4.html#E4:67"><i><font color="Green" title="E58">A4</font></i></a>, <a class="txt" href="aff_4.html#E7:67_1"><i><font color="Green" title="E64">A10</font></i></a>, <a class="txt" href="aff_4.html#E8:67_1"><i><font color="Green" title="E65">A11</font></i></a>, <a class="txt" href="aff_4.html#E9:67_1"><i><font color="Green" title="E66">A12</font></i></a>, <a class="txt" href="aff_4.html#E13:67_1"><i><font color="Green" title="E68">A19</font></i></a>, <a class="txt" href="aff_4.html#E3:67_1_2"><i><font color="Green" title="E72">A23</font></i></a>, <a class="txt" href="aff_4.html#E4:67_1_2"><i><font color="Green" title="E73">A24</font></i></a>, <a class="txt" href="aff_4.html#E7:67_1_2"><i><font color="Green" title="E76">A27</font></i></a>, <a class="txt" href="aff_4.html#E8:67_1_2"><i><font color="Green" title="E77">A28</font></i></a>, <a class="txt" href="aff_4.html#E66"><i><font color="Green" title="E53">Lm11</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="E16:67_1"/>
<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">b'</font>,<font color="Maroon" title="c7">c'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E3:67"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="aff_4.html#E4:67"><i><font color="Green" title="E58">A4</font></i></a>, <a class="ref" href="aff_1.html#T65" title="AFF_1:th.65">AFF_1:65</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="E8:67"/>
<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">b'</font>,<font color="Maroon" title="c7">c'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E2:67"><i><font color="Green" title="E56">A2</font></i></a>, <a class="txt" href="aff_4.html#E3:67"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="aff_4.html#E4:67"><i><font color="Green" title="E58">A4</font></i></a>, <a class="txt" href="aff_4.html#E5:67"><i><font color="Green" title="E59">A5</font></i></a>, <a class="txt" href="aff_4.html#E6:67"><i><font color="Green" title="E60">A6</font></i></a>, <a class="txt" href="aff_4.html#E66"><i><font color="Green" title="E53">Lm11</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>
