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

<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="incsp_1.html#NM4" title="INCSP_1:NM.4">IncSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">K</font>, <font color="Olive" title="b2">L</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">K</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">L</font> &amp;  ex <font color="Olive" title="b3">A</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Olive" title="b3">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> &amp; <font color="Olive" title="b3">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b2">L</font> ) holds <br/> <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Olive" title="b1">K</font>,<font color="Olive" title="b2">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Olive" title="b2">L</font>,<font color="Olive" title="b1">K</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">K</font>, <font color="Maroon" title="c3">L</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">K</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">L</font> &amp;  ex <font color="Olive" title="b1">A</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">K</font> &amp; <font color="Olive" title="b1">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">L</font> ) implies  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:86"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
<font color="Maroon" title="c2">K</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">L</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( for <font color="Olive" title="b1">A</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font>  holds <br/>(  not <font color="Olive" title="b1">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">K</font> or  not <font color="Olive" title="b1">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">L</font> ) or  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c4">P2</font> =  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">P1</font> =  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font>;<br/>
<span class="kw">given </span><font color="Maroon" title="c6">A</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font><span class="kw"> such that </span><a NAME="E3:86"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
<font color="Maroon" title="c6">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">K</font>
 <span class="kw">and </span><br/><a NAME="E4:86"/><span class="lab"><font color="Green" title="E50">A3</font></span>: 
<font color="Maroon" title="c6">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">L</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c7">C</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font><span class="kw"> such that </span><br/><a NAME="E6:86"/><span class="lab"><font color="Green" title="E51">A4</font></span>: 
<font color="Maroon" title="c6">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">C</font>
 <span class="kw">and </span><br/><a NAME="E7:86"/><span class="lab"><font color="Green" title="E52">A5</font></span>: 
<font color="Maroon" title="c7">C</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="incsp_1.html#E60"><span class="lab"><font color="Green" title="E36">Lm1</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">B</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font><span class="kw"> such that </span><br/><a NAME="E9:86"/><span class="lab"><font color="Green" title="E53">A6</font></span>: 
<font color="Maroon" title="c6">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">B</font>
 <span class="kw">and </span><br/><a NAME="E10:86"/><span class="lab"><font color="Green" title="E54">A7</font></span>: 
<font color="Maroon" title="c8">B</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="incsp_1.html#E60"><span class="lab"><font color="Green" title="E36">Lm1</font></span></a></span>;<br/>
<a NAME="E11:86"/><span class="lab"><font color="Green" title="E55">A8</font></span>: 
<font color="Maroon" title="c2">K</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:86"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E3:86"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E4:86"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="incsp_1.html#D22" target="_self" title="INCSP_1:def.22">Def22</a></span>;<br/>
<a NAME="E12:86"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A9</font></span>: 
<font color="Maroon" title="c8">B</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:86"><span class="lab"><font color="Green" title="E54">A7</font></span></a>, <a class="ref" href="incsp_1.html#D17" target="_self" title="INCSP_1:def.17">Def17</a></span>;<br/>
<a NAME="E13:86"/><span class="lab"><font color="Green" title="E57">A10</font></span>: 
<font color="Maroon" title="c2">K</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:86"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E3:86"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E4:86"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="incsp_1.html#D22" target="_self" title="INCSP_1:def.22">Def22</a></span>;<br/>
<a NAME="E14:86"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A11</font></span>: 
<font color="Maroon" title="c8">B</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:86"><span class="lab"><font color="Green" title="E54">A7</font></span></a>, <a class="ref" href="incsp_1.html#D17" target="_self" title="INCSP_1:def.17">Def17</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E59">A12</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="86_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:86_1"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c8">B</font>,<font color="Maroon" title="c7">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> is  <a href="incsp_1.html#V3" title="INCSP_1:attr.3">linear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">L1</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">S</font><span class="kw"> such that </span><br/><a NAME="E3:86_1"/><span class="lab"><font color="Green" title="E60">A13</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c8">B</font>,<font color="Maroon" title="c7">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c9">L1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incsp_1.html#D6" target="_self" title="INCSP_1:def.6">Def6</a></span>;<br/><a NAME="E4:86_1"/><span class="lab"><font color="Green" title="E61">A14</font></span>: 
<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">L1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:86_1"><span class="lab"><font color="Green" title="E60">A13</font></span></a>, <a class="ref" href="incsp_1.html#T12" target="_self" title="INCSP_1:th.12">Th12</a></span>;<br/><a NAME="E5:86_1"/>
<font color="Maroon" title="c7">C</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:86_1"><span class="lab"><font color="Green" title="E60">A13</font></span></a>, <a class="ref" href="incsp_1.html#T12" target="_self" title="INCSP_1:th.12">Th12</a></span>;<br/><a NAME="E6:86_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A15</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">C</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c9">L1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:86_1"><span class="lab"><font color="Green" title="E61">A14</font></span></a>, <a class="ref" href="incsp_1.html#T11" target="_self" title="INCSP_1:th.11">Th11</a></span>;<br/><a NAME="E7:86_1"/><span class="lab"><font color="Green" title="E63">A16</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c8">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c2">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:86"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E10:86"><span class="lab"><font color="Green" title="E54">A7</font></span></a>, <a class="ref" href="incsp_1.html#T11" target="_self" title="INCSP_1:th.11">Th11</a></span>;<br/><a NAME="E8:86_1"/>
<font color="Maroon" title="c8">B</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:86_1"><span class="lab"><font color="Green" title="E60">A13</font></span></a>, <a class="ref" href="incsp_1.html#T12" target="_self" title="INCSP_1:th.12">Th12</a></span>;<br/><a NAME="E9:86_1"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c8">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c9">L1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:86_1"><span class="lab"><font color="Green" title="E61">A14</font></span></a>, <a class="ref" href="incsp_1.html#T11" target="_self" title="INCSP_1:th.11">Th11</a></span>;<br/><a NAME="E10:86_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A17</font></span>: 
<font color="Maroon" title="c2">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">L1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:86"><span class="lab"><font color="Green" title="E53">A6</font></span></a>, <a class="txt" href="#E7:86_1"><span class="lab"><font color="Green" title="E63">A16</font></span></a>, <a class="ref" href="incsp_1.html#D10" target="_self" title="INCSP_1:def.10">Def10</a></span>;<br/><a NAME="E11:86_1"/>
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">C</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c3">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:86"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="txt" href="#E7:86"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="ref" href="incsp_1.html#T11" target="_self" title="INCSP_1:th.11">Th11</a></span>;<br/><span class="kw">hence </span><a NAME="E12:86_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:86"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E6:86"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E6:86_1"><span class="lab"><font color="Green" title="E62">A15</font></span></a>, <a class="txt" href="#E10:86_1"><span class="lab"><font color="Green" title="E64">A17</font></span></a>, <a class="ref" href="incsp_1.html#D10" target="_self" title="INCSP_1:def.10">Def10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E16:86"/>
<font color="Maroon" title="c3">L</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:86"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E3:86"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E4:86"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="incsp_1.html#D22" target="_self" title="INCSP_1:def.22">Def22</a></span>;<br/>
<a NAME="E17:86"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A18</font></span>: 
<font color="Maroon" title="c7">C</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:86"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="ref" href="incsp_1.html#D17" target="_self" title="INCSP_1:def.17">Def17</a></span>;<br/>
<a NAME="E18:86"/>
<font color="Maroon" title="c6">A</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:86"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E11:86"><span class="lab"><font color="Green" title="E55">A8</font></span></a>, <a class="ref" href="incsp_1.html#D17" target="_self" title="INCSP_1:def.17">Def17</a></span>;<br/>
<a NAME="E19:86"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A19</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c8">B</font>,<font color="Maroon" title="c7">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:86"><span class="lab"><font color="Green" title="E56">A9</font></span></a>, <a class="txt" href="#E17:86"><span class="lab"><font color="Green" title="E60">A18</font></span></a>, <a class="ref" href="incsp_1.html#T14" target="_self" title="INCSP_1:th.14">Th14</a></span>;<br/>
<a NAME="E20:86"/>
<font color="Maroon" title="c3">L</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:86"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E3:86"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E4:86"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="incsp_1.html#D22" target="_self" title="INCSP_1:def.22">Def22</a></span>;<br/>
<a NAME="E21:86"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A20</font></span>: 
<font color="Maroon" title="c7">C</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:86"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="ref" href="incsp_1.html#D17" target="_self" title="INCSP_1:def.17">Def17</a></span>;<br/>
<a NAME="E22:86"/>
<font color="Maroon" title="c6">A</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:86"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E13:86"><span class="lab"><font color="Green" title="E57">A10</font></span></a>, <a class="ref" href="incsp_1.html#D17" target="_self" title="INCSP_1:def.17">Def17</a></span>;<br/>
<a NAME="E23:86"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c8">B</font>,<font color="Maroon" title="c7">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:86"><span class="lab"><font color="Green" title="E58">A11</font></span></a>, <a class="txt" href="#E21:86"><span class="lab"><font color="Green" title="E62">A20</font></span></a>, <a class="ref" href="incsp_1.html#T14" target="_self" title="INCSP_1:th.14">Th14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E24:86"/>
 <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:86"><span class="lab"><font color="Green" title="E61">A19</font></span></a>, <a class="txt" href="#E15:86"><span class="lab"><font color="Green" title="E59">A12</font></span></a>, <a class="ref" href="incsp_1.html#D13" target="_self" title="INCSP_1:def.13">Def13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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