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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>;<br/><b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>;<br/><b>let </b><font color="Maroon" title="c3">X</font>, <font color="Maroon" title="c4">X'</font>, <font color="Maroon" title="c5">Y</font>, <font color="Maroon" title="c6">Y'</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font>;<br/><b>let </b><font color="Maroon" title="c7">p</font>, <font color="Maroon" title="c8">b</font>, <font color="Maroon" title="c9">c</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <span class="p1">(<span class="default"><a href="afproj.html#K13" title="AFPROJ:func.13">IncProjSp_of</a> <font color="Maroon" title="c1">AS</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c10">A</font>, <font color="Maroon" title="c11">K</font>, <font color="Maroon" title="c12">M</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <span class="p1">(<span class="default"><a href="afproj.html#K13" title="AFPROJ:func.13">IncProjSp_of</a> <font color="Maroon" title="c1">AS</font></span>)</span>;<br/>























<b>assume </b><b>that </b><br/><a NAME="E1:57"/><i><font color="Green" title="E46">A1</font></i>: 
( <font color="Maroon" title="c3">X</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c4">X'</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c5">Y</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a>  )
 <b>and </b><br/><a NAME="E2:57"/><i><font color="Green" title="E47">A2</font></i>: 
( <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">Y</font> &amp; <font color="Maroon" title="c4">X'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">Y</font> )
 <b>and </b><br/><a NAME="E3:57"/><i><font color="Green" title="E48">A3</font></i>: 
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">p</font> &amp; <font color="Maroon" title="c10">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">X</font>,1</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c11">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">X'</font>,1</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c10">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">K</font> )
 <b>and </b><br/><a NAME="E4:57"/><i><font color="Green" title="E49">A4</font></i>: 
( <font color="Maroon" title="c8">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">A</font> &amp; <font color="Maroon" title="c9">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">K</font> &amp; <font color="Maroon" title="c8">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">M</font> &amp; <font color="Maroon" title="c9">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">M</font> &amp; <font color="Maroon" title="c8">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">c</font> )
 <b>and </b><br/><a NAME="E5:57"/><i><font color="Green" title="E50">A5</font></i>: 
( <font color="Maroon" title="c12">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">Y'</font>,1</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c6">Y'</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  )
 ;<br/>

<div><i><font color="Green" title="E51">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:57_1"/>
<font color="Maroon" title="c8">b</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c13">y</font> = <font color="Maroon" title="c8">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> ;<br/><div><i><font color="Green" title="E52">A7</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:57_1_1"/>
<font color="Maroon" title="c9">c</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c14">z</font> = <font color="Maroon" title="c9">c</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> ;<br/><a NAME="E3:57_1_1"/><i><font color="Green" title="E53">A8</font></i>: 
( <font color="Maroon" title="c13">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Y'</font> &amp; <font color="Maroon" title="c14">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Y'</font> )
 <b>by </b><i><a class="txt" href="afproj.html#E4:57"><i><font color="Green" title="E49">A4</font></i></a>, <a class="txt" href="afproj.html#E5:57"><i><font color="Green" title="E50">A5</font></i></a>, <a class="ref" href="afproj.html#T26" target="_self" title="AFPROJ:th.26">Th26</a></i>;<br/><a NAME="E4:57_1_1"/><i><font color="Green" title="E54">A9</font></i>: 
( <font color="Maroon" title="c13">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> &amp; <font color="Maroon" title="c14">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X'</font> )
 <b>by </b><i><a class="txt" href="afproj.html#E3:57"><i><font color="Green" title="E48">A3</font></i></a>, <a class="txt" href="afproj.html#E4:57"><i><font color="Green" title="E49">A4</font></i></a>, <a class="ref" href="afproj.html#T26" target="_self" title="AFPROJ:th.26">Th26</a></i>;<br/><a NAME="E5:57_1_1"/>
<font color="Maroon" title="c6">Y'</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="c13">y</font>,<font color="Maroon" title="c14">z</font>
 <b>by </b><i><a class="txt" href="afproj.html#E4:57"><i><font color="Green" title="E49">A4</font></i></a>, <a class="txt" href="afproj.html#E5:57"><i><font color="Green" title="E50">A5</font></i></a>, <a class="txt" href="afproj.html#E3:57_1_1"><i><font color="Green" title="E53">A8</font></i></a>, <a class="ref" href="aff_1.html#T71" title="AFF_1:th.71">AFF_1:71</a></i>;<br/><b>hence </b><a NAME="E6:57_1_1"/>
<font color="Maroon" title="c6">Y'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">Y</font>
 <b>by </b><i><a class="txt" href="afproj.html#E1:57"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="afproj.html#E2:57"><i><font color="Green" title="E47">A2</font></i></a>, <a class="txt" href="afproj.html#E4:57"><i><font color="Green" title="E49">A4</font></i></a>, <a class="txt" href="afproj.html#E4:57_1_1"><i><font color="Green" title="E54">A9</font></i></a>, <a class="ref" href="aff_4.html#T19" title="AFF_4:th.19">AFF_4:19</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1_2"><b>now </b></a><div class="add"><b>given </b><font color="Maroon" title="c14">Xc</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><a NAME="E2:57_1_2"/><i><font color="Green" title="E53">A10</font></i>: 
( <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afproj.html#K5" title="AFPROJ:func.5">LDir</a> <font color="Maroon" title="c14">Xc</font> &amp; <font color="Maroon" title="c14">Xc</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  )
 ;<br/><a NAME="E3:57_1_2"/><i><font color="Green" title="E54">A11</font></i>: 
( <font color="Maroon" title="c13">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Y'</font> &amp; <font color="Maroon" title="c13">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> )
 <b>by </b><i><a class="txt" href="afproj.html#E3:57"><i><font color="Green" title="E48">A3</font></i></a>, <a class="txt" href="afproj.html#E4:57"><i><font color="Green" title="E49">A4</font></i></a>, <a class="txt" href="afproj.html#E5:57"><i><font color="Green" title="E50">A5</font></i></a>, <a class="ref" href="afproj.html#T26" target="_self" title="AFPROJ:th.26">Th26</a></i>;<br/><a NAME="E4:57_1_2"/>
<font color="Maroon" title="c14">Xc</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Maroon" title="c6">Y'</font>
 <b>by </b><i><a class="txt" href="afproj.html#E4:57"><i><font color="Green" title="E49">A4</font></i></a>, <a class="txt" href="afproj.html#E5:57"><i><font color="Green" title="E50">A5</font></i></a>, <a class="txt" href="afproj.html#E2:57_1_2"><i><font color="Green" title="E53">A10</font></i></a>, <a class="ref" href="afproj.html#T28" target="_self" title="AFPROJ:th.28">Th28</a></i>;<br/><a NAME="E5:57_1_2"/><b>then </b><i><font color="Green" title="E55">A12</font></i>: 
<font color="Maroon" title="c14">Xc</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c6">Y'</font>
 <b>by </b><i><a class="txt" href="afproj.html#E5:57"><i><font color="Green" title="E50">A5</font></i></a>, <a class="txt" href="afproj.html#E2:57_1_2"><i><font color="Green" title="E53">A10</font></i></a>, <a class="ref" href="aff_4.html#T40" title="AFF_4:th.40">AFF_4:40</a></i>;<br/><a NAME="E6:57_1_2"/>
<font color="Maroon" title="c14">Xc</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Maroon" title="c4">X'</font>
 <b>by </b><i><a class="txt" href="afproj.html#E1:57"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="afproj.html#E3:57"><i><font color="Green" title="E48">A3</font></i></a>, <a class="txt" href="afproj.html#E4:57"><i><font color="Green" title="E49">A4</font></i></a>, <a class="txt" href="afproj.html#E2:57_1_2"><i><font color="Green" title="E53">A10</font></i></a>, <a class="ref" href="afproj.html#T28" target="_self" title="AFPROJ:th.28">Th28</a></i>;<br/><a NAME="E7:57_1_2"/><b>then </b>
<font color="Maroon" title="c14">Xc</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c4">X'</font>
 <b>by </b><i><a class="txt" href="afproj.html#E1:57"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="afproj.html#E2:57_1_2"><i><font color="Green" title="E53">A10</font></i></a>, <a class="ref" href="aff_4.html#T40" title="AFF_4:th.40">AFF_4:40</a></i>;<br/><a NAME="E8:57_1_2"/><b>then </b>
<font color="Maroon" title="c4">X'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c6">Y'</font>
 <b>by </b><i><a class="txt" href="afproj.html#E5:57_1_2"><i><font color="Green" title="E55">A12</font></i></a>, <a class="ref" href="aff_1.html#T58" title="AFF_1:th.58">AFF_1:58</a></i>;<br/><a NAME="E9:57_1_2"/><b>then </b>
<font color="Maroon" title="c6">Y'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">y</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c4">X'</font>
 <b>by </b><i><a class="txt" href="afproj.html#E1:57"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="afproj.html#E3:57_1_2"><i><font color="Green" title="E54">A11</font></i></a>, <a class="ref" href="aff_4.html#D3" title="AFF_4:def.3">AFF_4:def 3</a></i>;<br/><b>hence </b><a NAME="E10:57_1_2"/>
<font color="Maroon" title="c6">Y'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">Y</font>
 <b>by </b><i><a class="txt" href="afproj.html#E1:57"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="afproj.html#E2:57"><i><font color="Green" title="E47">A2</font></i></a>, <a class="txt" href="afproj.html#E3:57_1_2"><i><font color="Green" title="E54">A11</font></i></a>, <a class="ref" href="aff_4.html#T28" title="AFF_4:th.28">AFF_4:28</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:57_1"/>
<font color="Maroon" title="c6">Y'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">Y</font>
 <b>by </b><i><a class="txt" href="afproj.html#E3:57_1"><i><font color="Green" title="E52">A7</font></i></a>, <a class="ref" href="afproj.html#T20" target="_self" title="AFPROJ:th.20">Th20</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2"><b>now </b></a><div class="add"><b>given </b><font color="Maroon" title="c13">Xb</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><a NAME="E2:57_2"/><i><font color="Green" title="E52">A13</font></i>: 
( <font color="Maroon" title="c8">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afproj.html#K5" title="AFPROJ:func.5">LDir</a> <font color="Maroon" title="c13">Xb</font> &amp; <font color="Maroon" title="c13">Xb</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  )
 ;<br/><div><i><font color="Green" title="E53">A14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:57_2_1"/>
<font color="Maroon" title="c9">c</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c14">y</font> = <font color="Maroon" title="c9">c</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> ;<br/><a NAME="E3:57_2_1"/><i><font color="Green" title="E54">A15</font></i>: 
( <font color="Maroon" title="c14">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Y'</font> &amp; <font color="Maroon" title="c14">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X'</font> )
 <b>by </b><i><a class="txt" href="afproj.html#E3:57"><i><font color="Green" title="E48">A3</font></i></a>, <a class="txt" href="afproj.html#E4:57"><i><font color="Green" title="E49">A4</font></i></a>, <a class="txt" href="afproj.html#E5:57"><i><font color="Green" title="E50">A5</font></i></a>, <a class="ref" href="afproj.html#T26" target="_self" title="AFPROJ:th.26">Th26</a></i>;<br/><a NAME="E4:57_2_1"/>
<font color="Maroon" title="c13">Xb</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Maroon" title="c6">Y'</font>
 <b>by </b><i><a class="txt" href="afproj.html#E4:57"><i><font color="Green" title="E49">A4</font></i></a>, <a class="txt" href="afproj.html#E5:57"><i><font color="Green" title="E50">A5</font></i></a>, <a class="txt" href="afproj.html#E2:57_2"><i><font color="Green" title="E52">A13</font></i></a>, <a class="ref" href="afproj.html#T28" target="_self" title="AFPROJ:th.28">Th28</a></i>;<br/><a NAME="E5:57_2_1"/><b>then </b><i><font color="Green" title="E55">A16</font></i>: 
<font color="Maroon" title="c13">Xb</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c6">Y'</font>
 <b>by </b><i><a class="txt" href="afproj.html#E5:57"><i><font color="Green" title="E50">A5</font></i></a>, <a class="txt" href="afproj.html#E2:57_2"><i><font color="Green" title="E52">A13</font></i></a>, <a class="ref" href="aff_4.html#T40" title="AFF_4:th.40">AFF_4:40</a></i>;<br/><a NAME="E6:57_2_1"/>
<font color="Maroon" title="c13">Xb</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="txt" href="afproj.html#E1:57"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="afproj.html#E3:57"><i><font color="Green" title="E48">A3</font></i></a>, <a class="txt" href="afproj.html#E4:57"><i><font color="Green" title="E49">A4</font></i></a>, <a class="txt" href="afproj.html#E2:57_2"><i><font color="Green" title="E52">A13</font></i></a>, <a class="ref" href="afproj.html#T28" target="_self" title="AFPROJ:th.28">Th28</a></i>;<br/><a NAME="E7:57_2_1"/><b>then </b>
<font color="Maroon" title="c13">Xb</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="txt" href="afproj.html#E1:57"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="afproj.html#E2:57_2"><i><font color="Green" title="E52">A13</font></i></a>, <a class="ref" href="aff_4.html#T40" title="AFF_4:th.40">AFF_4:40</a></i>;<br/><a NAME="E8:57_2_1"/><b>then </b>
<font color="Maroon" title="c3">X</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c6">Y'</font>
 <b>by </b><i><a class="txt" href="afproj.html#E5:57_2_1"><i><font color="Green" title="E55">A16</font></i></a>, <a class="ref" href="aff_1.html#T58" title="AFF_1:th.58">AFF_1:58</a></i>;<br/><a NAME="E9:57_2_1"/><b>then </b>
<font color="Maroon" title="c6">Y'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="txt" href="afproj.html#E1:57"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="afproj.html#E3:57_2_1"><i><font color="Green" title="E54">A15</font></i></a>, <a class="ref" href="aff_4.html#D3" title="AFF_4:def.3">AFF_4:def 3</a></i>;<br/><b>hence </b><a NAME="E10:57_2_1"/>
<font color="Maroon" title="c6">Y'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">Y</font>
 <b>by </b><i><a class="txt" href="afproj.html#E1:57"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="afproj.html#E2:57"><i><font color="Green" title="E47">A2</font></i></a>, <a class="txt" href="afproj.html#E3:57_2_1"><i><font color="Green" title="E54">A15</font></i></a>, <a class="ref" href="aff_4.html#T28" title="AFF_4:th.28">AFF_4:28</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_2"><b>now </b></a><div class="add"><b>given </b><font color="Maroon" title="c14">Xc</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><a NAME="E2:57_2_2"/><i><font color="Green" title="E54">A17</font></i>: 
( <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afproj.html#K5" title="AFPROJ:func.5">LDir</a> <font color="Maroon" title="c14">Xc</font> &amp; <font color="Maroon" title="c14">Xc</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  )
 ;<br/><a NAME="E3:57_2_2"/>
( <font color="Maroon" title="c14">Xc</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Maroon" title="c6">Y'</font> &amp; <font color="Maroon" title="c13">Xb</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Maroon" title="c6">Y'</font> )
 <b>by </b><i><a class="txt" href="afproj.html#E4:57"><i><font color="Green" title="E49">A4</font></i></a>, <a class="txt" href="afproj.html#E5:57"><i><font color="Green" title="E50">A5</font></i></a>, <a class="txt" href="afproj.html#E2:57_2"><i><font color="Green" title="E52">A13</font></i></a>, <a class="txt" href="afproj.html#E2:57_2_2"><i><font color="Green" title="E54">A17</font></i></a>, <a class="ref" href="afproj.html#T28" target="_self" title="AFPROJ:th.28">Th28</a></i>;<br/><a NAME="E4:57_2_2"/><b>then </b>
( <font color="Maroon" title="c14">Xc</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c6">Y'</font> &amp; <font color="Maroon" title="c13">Xb</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c6">Y'</font> )
 <b>by </b><i><a class="txt" href="afproj.html#E5:57"><i><font color="Green" title="E50">A5</font></i></a>, <a class="txt" href="afproj.html#E2:57_2"><i><font color="Green" title="E52">A13</font></i></a>, <a class="txt" href="afproj.html#E2:57_2_2"><i><font color="Green" title="E54">A17</font></i></a>, <a class="ref" href="aff_4.html#T40" title="AFF_4:th.40">AFF_4:40</a></i>;<br/><a NAME="E5:57_2_2"/><b>then </b>
<font color="Maroon" title="c14">Xc</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Xb</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T58" title="AFF_1:th.58">AFF_1:58</a></i>;<br/><b>hence </b><a NAME="E6:57_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="afproj.html#E4:57"><i><font color="Green" title="E49">A4</font></i></a>, <a class="txt" href="afproj.html#E2:57_2"><i><font color="Green" title="E52">A13</font></i></a>, <a class="txt" href="afproj.html#E2:57_2_2"><i><font color="Green" title="E54">A17</font></i></a>, <a class="ref" href="afproj.html#T11" target="_self" title="AFPROJ:th.11">Th11</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:57_2"/>
<font color="Maroon" title="c6">Y'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">Y</font>
 <b>by </b><i><a class="txt" href="afproj.html#E3:57_2"><i><font color="Green" title="E53">A14</font></i></a>, <a class="ref" href="afproj.html#T20" target="_self" title="AFPROJ:th.20">Th20</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:57"/>
<font color="Maroon" title="c6">Y'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">Y</font>
 <b>by </b><i><a class="txt" href="afproj.html#E6:57"><i><font color="Green" title="E51">A6</font></i></a>, <a class="ref" href="afproj.html#T20" target="_self" title="AFPROJ:th.20">Th20</a></i>;<br/>


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