<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">CPS</font> be   <a href="anproj_2.html#NM1" title="ANPROJ_2:NM.1">CollProjectiveSpace</a>;<br/>

<b>assume </b><a NAME="E1:22"/><i><font color="Green" title="E22">A1</font></i>: 
for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">r2</font>, <font color="Olive" title="b3">q</font>, <font color="Olive" title="b4">r1</font>, <font color="Olive" title="b5">q1</font>, <font color="Olive" title="b6">p</font>, <font color="Olive" title="b7">r</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">CPS</font>  st <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">r2</font>,<font color="Olive" title="b3">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b4">r1</font>,<font color="Olive" title="b5">q1</font>,<font color="Olive" title="b3">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b4">r1</font>,<font color="Olive" title="b6">p</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">r2</font>,<font color="Olive" title="b5">q1</font>,<font color="Olive" title="b6">p</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b5">q1</font>,<font color="Olive" title="b7">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">r2</font>,<font color="Olive" title="b4">r1</font>,<font color="Olive" title="b7">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b6">p</font>,<font color="Olive" title="b3">q</font>,<font color="Olive" title="b7">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">r2</font>,<font color="Olive" title="b5">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">r2</font>,<font color="Olive" title="b4">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b4">r1</font>,<font color="Olive" title="b5">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  holds <br/><font color="Olive" title="b2">r2</font>,<font color="Olive" title="b4">r1</font>,<font color="Olive" title="b5">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ;<br/>

<b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">r</font>, <font color="Maroon" title="c5">s</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="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c9">L</font>, <font color="Maroon" title="c10">Q</font>, <font color="Maroon" title="c11">R</font>, <font color="Maroon" title="c12">S</font>, <font color="Maroon" title="c13">A</font>, <font color="Maroon" title="c14">B</font>, <font color="Maroon" title="c15">C</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E2:22"/><i><font color="Green" title="E23">A2</font></i>: 
( not <font color="Maroon" title="c3">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L</font> &amp; not <font color="Maroon" title="c4">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L</font> &amp; not <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">Q</font> &amp; not <font color="Maroon" title="c5">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">Q</font> &amp; not <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">R</font> &amp; not <font color="Maroon" title="c4">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">R</font> &amp; not <font color="Maroon" title="c3">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">S</font> &amp; not <font color="Maroon" title="c5">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">S</font> )
 <b>and </b><br/><a NAME="E3:22"/><i><font color="Green" title="E24">A3</font></i>: 
( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">s</font> <a href="incproj.html#R4" title="INCPROJ:pred.4">on</a> <font color="Maroon" title="c9">L</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">r</font> <a href="incproj.html#R4" title="INCPROJ:pred.4">on</a> <font color="Maroon" title="c10">Q</font> &amp; <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">s</font> <a href="incproj.html#R4" title="INCPROJ:pred.4">on</a> <font color="Maroon" title="c11">R</font> &amp; <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">r</font> <a href="incproj.html#R4" title="INCPROJ:pred.4">on</a> <font color="Maroon" title="c12">S</font> &amp; <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> <a href="incproj.html#R4" title="INCPROJ:pred.4">on</a> <font color="Maroon" title="c13">A</font> &amp; <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c4">r</font>,<font color="Maroon" title="c5">s</font> <a href="incproj.html#R4" title="INCPROJ:pred.4">on</a> <font color="Maroon" title="c14">B</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="incproj.html#R3" title="INCPROJ:pred.3">on</a> <font color="Maroon" title="c15">C</font> )
 ;<br/>

<b>assume </b><a NAME="E4:22"/><i><font color="Green" title="E25">A4</font></i>: 
<font color="Maroon" title="c8">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">C</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c16">p'</font> = <font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c17">q'</font> = <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c18">r'</font> = <font color="Maroon" title="c4">r</font>, <font color="Maroon" title="c19">s'</font> = <font color="Maroon" title="c5">s</font>, <font color="Maroon" title="c20">a'</font> = <font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c21">b'</font> = <font color="Maroon" title="c7">b</font>, <font color="Maroon" title="c22">c'</font> = <font color="Maroon" title="c8">c</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">CPS</font> ;<br/>
<a NAME="E6:22"/>
( <font color="Maroon" title="c6">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">C</font> &amp; <font color="Maroon" title="c7">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">C</font> )
 
<b>by </b><i><a class="txt" href="incproj.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="incproj.html#D7" target="_self" title="INCPROJ:def.7">Def7</a></i>;<br/>
<a NAME="E7:22"/><b>then </b><i><font color="Green" title="E26">A5</font></i>: 
<font color="Maroon" title="c20">a'</font>,<font color="Maroon" title="c21">b'</font>,<font color="Maroon" title="c22">c'</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="incproj.html#E4:22"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></i>;<br/>
<a NAME="E8:22"/><i><font color="Green" title="E27">A6</font></i>: 
( <font color="Maroon" title="c6">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L</font> &amp; <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L</font> &amp; <font color="Maroon" title="c5">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L</font> &amp; <font color="Maroon" title="c6">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">Q</font> &amp; <font color="Maroon" title="c3">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">Q</font> &amp; <font color="Maroon" title="c4">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">Q</font> &amp; <font color="Maroon" title="c7">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">R</font> &amp; <font color="Maroon" title="c3">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">R</font> &amp; <font color="Maroon" title="c5">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">R</font> &amp; <font color="Maroon" title="c7">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">S</font> &amp; <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">S</font> &amp; <font color="Maroon" title="c4">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">S</font> &amp; <font color="Maroon" title="c8">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">A</font> &amp; <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">A</font> &amp; <font color="Maroon" title="c3">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">A</font> &amp; <font color="Maroon" title="c8">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">B</font> &amp; <font color="Maroon" title="c4">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">B</font> &amp; <font color="Maroon" title="c5">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">B</font> )
 
<b>by </b><i><a class="txt" href="incproj.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="incproj.html#D8" target="_self" title="INCPROJ:def.8">Def8</a></i>;<br/>
<a NAME="E9:22"/><b>then </b><i><font color="Green" title="E28">A7</font></i>: 
( <font color="Maroon" title="c16">p'</font>,<font color="Maroon" title="c18">r'</font>,<font color="Maroon" title="c21">b'</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c19">s'</font>,<font color="Maroon" title="c17">q'</font>,<font color="Maroon" title="c21">b'</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c16">p'</font>,<font color="Maroon" title="c19">s'</font>,<font color="Maroon" title="c20">a'</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c18">r'</font>,<font color="Maroon" title="c17">q'</font>,<font color="Maroon" title="c20">a'</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c16">p'</font>,<font color="Maroon" title="c17">q'</font>,<font color="Maroon" title="c22">c'</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c18">r'</font>,<font color="Maroon" title="c19">s'</font>,<font color="Maroon" title="c22">c'</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 
<b>by </b><i><a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></i>;<br/>
<div><i><font color="Green" title="E29">A8</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1"/>
<font color="Maroon" title="c16">p'</font>,<font color="Maroon" title="c18">r'</font>,<font color="Maroon" title="c17">q'</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ;<br/><a NAME="E2:22_1"/><b>then </b><i><font color="Green" title="E30">A9</font></i>: 
 ex <font color="Olive" title="b1">K</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span> st <br/>( <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c4">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c3">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> )
 <b>by </b><i><a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></i>;<br/><b>hence </b><a NAME="E3:22_1"/>
<font color="Maroon" title="c3">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">S</font>
 <b>by </b><i><a class="txt" href="incproj.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="incproj.html#E8:22"><i><font color="Green" title="E27">A6</font></i></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</a></i>;<br/><b>thus </b><a NAME="E4:22_1"/>
contradiction
 <b>by </b><i><a class="txt" href="incproj.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="incproj.html#E8:22"><i><font color="Green" title="E27">A6</font></i></a>, <a class="txt" href="incproj.html#E2:22_1"><i><font color="Green" title="E30">A9</font></i></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E30">A10</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_2"/>
<font color="Maroon" title="c16">p'</font>,<font color="Maroon" title="c18">r'</font>,<font color="Maroon" title="c19">s'</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ;<br/><a NAME="E2:22_2"/><b>then </b><i><font color="Green" title="E31">A11</font></i>: 
 ex <font color="Olive" title="b1">K</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span> st <br/>( <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c4">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c5">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> )
 <b>by </b><i><a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></i>;<br/><b>hence </b><a NAME="E3:22_2"/>
<font color="Maroon" title="c5">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">S</font>
 <b>by </b><i><a class="txt" href="incproj.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="incproj.html#E8:22"><i><font color="Green" title="E27">A6</font></i></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</a></i>;<br/><b>thus </b><a NAME="E4:22_2"/>
contradiction
 <b>by </b><i><a class="txt" href="incproj.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="incproj.html#E8:22"><i><font color="Green" title="E27">A6</font></i></a>, <a class="txt" href="incproj.html#E2:22_2"><i><font color="Green" title="E31">A11</font></i></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E31">A12</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_3"/>
<font color="Maroon" title="c16">p'</font>,<font color="Maroon" title="c19">s'</font>,<font color="Maroon" title="c17">q'</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ;<br/><a NAME="E2:22_3"/><b>then </b><i><font color="Green" title="E32">A13</font></i>: 
 ex <font color="Olive" title="b1">K</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span> st <br/>( <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c5">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c3">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> )
 <b>by </b><i><a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></i>;<br/><b>hence </b><a NAME="E3:22_3"/>
<font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">R</font>
 <b>by </b><i><a class="txt" href="incproj.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="incproj.html#E8:22"><i><font color="Green" title="E27">A6</font></i></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</a></i>;<br/><b>thus </b><a NAME="E4:22_3"/>
contradiction
 <b>by </b><i><a class="txt" href="incproj.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="incproj.html#E8:22"><i><font color="Green" title="E27">A6</font></i></a>, <a class="txt" href="incproj.html#E2:22_3"><i><font color="Green" title="E32">A13</font></i></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_4"/>
<font color="Maroon" title="c18">r'</font>,<font color="Maroon" title="c19">s'</font>,<font color="Maroon" title="c17">q'</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ;<br/><a NAME="E2:22_4"/><b>then </b><i><font color="Green" title="E32">A14</font></i>: 
 ex <font color="Olive" title="b1">K</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span> st <br/>( <font color="Maroon" title="c4">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c5">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c3">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> )
 <b>by </b><i><a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></i>;<br/><b>hence </b><a NAME="E3:22_4"/>
<font color="Maroon" title="c4">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">R</font>
 <b>by </b><i><a class="txt" href="incproj.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="incproj.html#E8:22"><i><font color="Green" title="E27">A6</font></i></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</a></i>;<br/><b>thus </b><a NAME="E4:22_4"/>
contradiction
 <b>by </b><i><a class="txt" href="incproj.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="incproj.html#E8:22"><i><font color="Green" title="E27">A6</font></i></a>, <a class="txt" href="incproj.html#E2:22_4"><i><font color="Green" title="E32">A14</font></i></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E14:22"/>
contradiction
 <b>by </b><i><a class="txt" href="incproj.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="incproj.html#E7:22"><i><font color="Green" title="E26">A5</font></i></a>, <a class="txt" href="incproj.html#E9:22"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="incproj.html#E10:22"><i><font color="Green" title="E29">A8</font></i></a>, <a class="txt" href="incproj.html#E11:22"><i><font color="Green" title="E30">A10</font></i></a>, <a class="txt" href="incproj.html#E12:22"><i><font color="Green" title="E31">A12</font></i></a></i>;<br/>


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