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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> 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="b2">X</font>, <font color="Olive" title="b3">M</font>, <font color="Olive" title="b4">N</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="b2">X</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a>  &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">X</font> &amp; <font color="Olive" title="b3">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">X</font> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b4">N</font> &amp; ( <font color="Olive" title="b3">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Olive" title="b4">N</font> or <font color="Olive" title="b4">N</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Olive" title="b3">M</font> ) holds <br/><font color="Olive" title="b4">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">X</font></span><br/><b>let </b><font color="Maroon" title="c2">a</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">X</font>, <font color="Olive" title="b2">M</font>, <font color="Olive" title="b3">N</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">X</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">X</font> &amp; <font color="Olive" title="b2">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">X</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">N</font> &amp; ( <font color="Olive" title="b2">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Olive" title="b3">N</font> or <font color="Olive" title="b3">N</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Olive" title="b2">M</font> ) holds <br/><font color="Olive" title="b3">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">X</font></span><br/><b>let </b><font color="Maroon" title="c3">X</font>, <font color="Maroon" title="c4">M</font>, <font color="Maroon" title="c5">N</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="c3">X</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> &amp; <font color="Maroon" title="c4">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">N</font> &amp; ( <font color="Maroon" title="c4">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c5">N</font> or <font color="Maroon" title="c5">N</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c4">M</font> ) implies <font color="Maroon" title="c5">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font> )</span><br/>









<b>assume </b><b>that </b><br/><a NAME="E1:31"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c3">X</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a> 
 <b>and </b><br/><a NAME="E2:31"/><i><font color="Green" title="E27">A2</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> &amp; <font color="Maroon" title="c4">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font> )
 <b>and </b><br/><a NAME="E3:31"/><i><font color="Green" title="E28">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="c5">N</font>
 <b>and </b><br/><a NAME="E4:31"/><i><font color="Green" title="E29">A4</font></i>: 
( <font color="Maroon" title="c4">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c5">N</font> or <font color="Maroon" title="c5">N</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c4">M</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font></span><br/>

<a NAME="E5:31"/><i><font color="Green" title="E30">A5</font></i>: 
( <font color="Maroon" title="c4">M</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c5">N</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#E4:31"><i><font color="Green" title="E29">A4</font></i></a>, <a class="ref" href="aff_1.html#T50" title="AFF_1:th.50">AFF_1:50</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">K</font>, <font color="Maroon" title="c7">P</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="E7:31"/><i><font color="Green" title="E31">A6</font></i>: 
( <font color="Maroon" title="c6">K</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c7">P</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  )
 <b>and </b><br/><a NAME="E8:31"/><i><font color="Green" title="E32">A7</font></i>: 
not <font color="Maroon" title="c6">K</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c7">P</font>
 <b>and </b><br/><a NAME="E9:31"/><i><font color="Green" title="E33">A8</font></i>: 
<font color="Maroon" title="c3">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_4.html#K1" title="AFF_4:func.1">Plane</a> <font color="Maroon" title="c6">K</font>,<font color="Maroon" title="c7">P</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:31"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="aff_4.html#D2" target="_self" title="AFF_4:def.2">Def2</a></i>;<br/>
<div><i><font color="Green" title="E34">A9</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:31_1"/>
<font color="Maroon" title="c6">K</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c4">M</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font></span><br/><a NAME="E2:31_1"/><b>then </b>
<font color="Maroon" title="c6">K</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c5">N</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E4:31"><i><font color="Green" title="E29">A4</font></i></a>, <a class="ref" href="aff_1.html#T58" title="AFF_1:th.58">AFF_1:58</a></i>;<br/><b>hence </b><a NAME="E3:31_1"/>
<font color="Maroon" title="c5">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E2:31"><i><font color="Green" title="E27">A2</font></i></a>, <a class="txt" href="aff_4.html#E3:31"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="aff_4.html#E7:31"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="aff_4.html#E9:31"><i><font color="Green" title="E33">A8</font></i></a>, <a class="txt" href="aff_4.html#E24"><i><font color="Green" title="E18">Lm4</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="31_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:31_2"/><i><font color="Green" title="E35">A10</font></i>: 
not <font color="Maroon" title="c6">K</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c4">M</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font></span><br/><a NAME="E2:31_2"/><b>then </b><i><font color="Green" title="E36">A11</font></i>: 
<font color="Maroon" title="c3">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_4.html#K1" title="AFF_4:func.1">Plane</a> <font color="Maroon" title="c6">K</font>,<font color="Maroon" title="c4">M</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E2:31"><i><font color="Green" title="E27">A2</font></i></a>, <a class="txt" href="aff_4.html#E5:31"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="aff_4.html#E7:31"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="aff_4.html#E8:31"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="aff_4.html#E9:31"><i><font color="Green" title="E33">A8</font></i></a>, <a class="ref" href="aff_4.html#T20" target="_self" title="AFF_4:th.20">Th20</a></i>;<br/><a NAME="E3:31_2"/><i><font color="Green" title="E37">A12</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_4.html#K1" title="AFF_4:func.1">Plane</a> <font color="Maroon" title="c6">K</font>,<font color="Maroon" title="c4">M</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E2:31"><i><font color="Green" title="E27">A2</font></i></a>, <a class="txt" href="aff_4.html#E5:31"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="aff_4.html#E7:31"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="aff_4.html#E8:31"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="aff_4.html#E9:31"><i><font color="Green" title="E33">A8</font></i></a>, <a class="txt" href="aff_4.html#E1:31_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="ref" href="aff_4.html#T20" target="_self" title="AFF_4:th.20">Th20</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:31_2_1"/><i><font color="Green" title="E38">A13</font></i>: 
<font color="Maroon" title="c4">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">N</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font></span><br/><b>consider </b><font color="Maroon" title="c8">a'</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="E3:31_2_1"/><i><font color="Green" title="E39">A14</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c8">a'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c6">K</font>
 <b>and </b><br/><a NAME="E4:31_2_1"/><i><font color="Green" title="E40">A15</font></i>: 
<font color="Maroon" title="c8">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E3:31_2"><i><font color="Green" title="E37">A12</font></i></a>, <a class="txt" href="aff_4.html#E17"><i><font color="Green" title="E14">Lm3</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c9">b'</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="E6:31_2_1"/><i><font color="Green" title="E41">A16</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">b'</font>
 <b>and </b><br/><a NAME="E7:31_2_1"/><i><font color="Green" title="E42">A17</font></i>: 
<font color="Maroon" title="c9">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E5:31"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="aff_1.html#T32" title="AFF_1:th.32">AFF_1:32</a></i>;<br/><b>consider </b><font color="Maroon" title="c10">b</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="E9:31_2_1"/><i><font color="Green" title="E43">A18</font></i>: 
( <font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c10">b</font> &amp; <font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c9">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c10">b</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E10:31_2_1"/><i><font color="Green" title="E44">A19</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="c8">a'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E3:31"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="aff_4.html#E4:31"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="aff_4.html#E1:31_2_1"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="aff_4.html#E4:31_2_1"><i><font color="Green" title="E40">A15</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>;<br/><a NAME="E11:31_2_1"/><i><font color="Green" title="E45">A20</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="c10">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:31_2_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</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="E2:31_2_1_1"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c8">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c9">b'</font>
 
<b>by </b><i><a class="txt" href="aff_4.html#E9:31_2_1"><i><font color="Green" title="E43">A18</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E3:31_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c9">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:31_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E5:31_2_1_1"/><b>then </b>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font>
 
<b>by </b><i><a class="txt" href="aff_4.html#E5:31"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="aff_4.html#E4:31_2_1"><i><font color="Green" title="E40">A15</font></i></a>, <a class="txt" href="aff_4.html#E6:31_2_1"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="aff_4.html#E7:31_2_1"><i><font color="Green" title="E42">A17</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<b>hence </b><a NAME="E6:31_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_4.html#E3:31"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="aff_4.html#E4:31"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="aff_4.html#E1:31_2_1"><i><font color="Green" title="E38">A13</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</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="E12:31_2_1"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c10">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">M</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E5:31"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="aff_4.html#E4:31_2_1"><i><font color="Green" title="E40">A15</font></i></a>, <a class="txt" href="aff_4.html#E6:31_2_1"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="aff_4.html#E7:31_2_1"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="aff_4.html#E9:31_2_1"><i><font color="Green" title="E43">A18</font></i></a>, <a class="ref" href="aff_1.html#T46" title="AFF_1:th.46">AFF_1:46</a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E13:31_2_1"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c10">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c5">N</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E4:31"><i><font color="Green" title="E29">A4</font></i></a>, <a class="ref" href="aff_4.html#T3" target="_self" title="AFF_4:th.3">Th3</a></i>;<br/><a NAME="E14:31_2_1"/><b>then </b><i><font color="Green" title="E46">A21</font></i>: 
<font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">N</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E3:31"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="aff_4.html#T2" target="_self" title="AFF_4:th.2">Th2</a></i>;<br/><a NAME="E15:31_2_1"/>
<font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c9">b'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c6">K</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E3:31_2_1"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="aff_4.html#E9:31_2_1"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="aff_4.html#E10:31_2_1"><i><font color="Green" title="E44">A19</font></i></a>, <a class="ref" href="aff_4.html#T4" target="_self" title="AFF_4:th.4">Th4</a></i>;<br/><a NAME="E16:31_2_1"/><b>then </b>
<font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_4.html#K1" title="AFF_4:func.1">Plane</a> <font color="Maroon" title="c6">K</font>,<font color="Maroon" title="c4">M</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E7:31_2_1"><i><font color="Green" title="E42">A17</font></i></a></i>;<br/><b>hence </b><a NAME="E17:31_2_1"/>
<font color="Maroon" title="c5">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E2:31"><i><font color="Green" title="E27">A2</font></i></a>, <a class="txt" href="aff_4.html#E3:31"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="aff_4.html#E5:31"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="aff_4.html#E7:31"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="aff_4.html#E2:31_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="aff_4.html#E11:31_2_1"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="aff_4.html#E14:31_2_1"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="aff_4.html#E25"><i><font color="Green" title="E19">Lm5</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="E5:31_2"/>
<font color="Maroon" title="c5">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E2:31"><i><font color="Green" title="E27">A2</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="E12:31"/>
<font color="Maroon" title="c5">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E10:31"><i><font color="Green" title="E34">A9</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>
