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<span class="kw">let </span><font color="Maroon" title="c1">IPP</font> be   <a href="incproj.html#V8" title="INCPROJ:attr.8">Fanoian</a>  <a href="incproj.html#NM2" title="INCPROJ:NM.2">IncProjSp</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r</font>, <font color="Olive" title="b4">s</font>, <font color="Olive" title="b5">a</font>, <font color="Olive" title="b6">b</font>, <font color="Olive" title="b7">c</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font> ex <font color="Olive" title="b8">A</font>, <font color="Olive" title="b9">B</font>, <font color="Olive" title="b10">C</font>, <font color="Olive" title="b11">Q</font>, <font color="Olive" title="b12">L</font>, <font color="Olive" title="b13">R</font>, <font color="Olive" title="b14">S</font>, <font color="Olive" title="b15">D</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> ex <font color="Olive" title="b16">d</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( not <font color="Olive" title="b2">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b12">L</font> &amp; not <font color="Olive" title="b3">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b12">L</font> &amp; not <font color="Olive" title="b1">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b11">Q</font> &amp; not <font color="Olive" title="b4">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b11">Q</font> &amp; not <font color="Olive" title="b1">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b13">R</font> &amp; not <font color="Olive" title="b3">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b13">R</font> &amp; not <font color="Olive" title="b2">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b14">S</font> &amp; not <font color="Olive" title="b4">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b14">S</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b5">a</font>,<font color="Olive" title="b1">p</font>,<font color="Olive" title="b4">s</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="Olive" title="b12">L</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b5">a</font>,<font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">r</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="Olive" title="b11">Q</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b6">b</font>,<font color="Olive" title="b2">q</font>,<font color="Olive" title="b4">s</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="Olive" title="b13">R</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b6">b</font>,<font color="Olive" title="b1">p</font>,<font color="Olive" title="b3">r</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="Olive" title="b14">S</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b7">c</font>,<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</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="Olive" title="b8">A</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b7">c</font>,<font color="Olive" title="b3">r</font>,<font color="Olive" title="b4">s</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="Olive" title="b9">B</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b5">a</font>,<font color="Olive" title="b6">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="Olive" title="b10">C</font> &amp; not <font color="Olive" title="b7">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b10">C</font> &amp; <font color="Olive" title="b6">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b15">D</font> &amp; <font color="Olive" title="b7">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b15">D</font> &amp; <font color="Olive" title="b10">C</font>,<font color="Olive" title="b15">D</font>,<font color="Olive" title="b13">R</font>,<font color="Olive" title="b14">S</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_different</a>  &amp; <font color="Olive" title="b16">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b8">A</font> &amp; <font color="Olive" title="b7">c</font>,<font color="Olive" title="b16">d</font>,<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_different</a>  )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c2">r</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font>, <font color="Maroon" title="c3">A</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E2:17"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
not <font color="Maroon" title="c2">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D11" title="INCPROJ:def.11">INCPROJ:def 11</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">p</font>, <font color="Maroon" title="c5">q</font>, <font color="Maroon" title="c6">c</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E4:17"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">q</font>
 <span class="kw">and </span><br/><a NAME="E5:17"/><span class="lab"><font color="Green" title="E14">A3</font></span>: 
<font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">c</font>
 <span class="kw">and </span><br/><a NAME="E6:17"/><span class="lab"><font color="Green" title="E15">A4</font></span>: 
<font color="Maroon" title="c6">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">p</font>
 <span class="kw">and </span><br/><a NAME="E7:17"/><span class="lab"><font color="Green" title="E16">A5</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">and </span><br/><a NAME="E8:17"/><span class="lab"><font color="Green" title="E17">A6</font></span>: 
<font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">and </span><br/><a NAME="E9:17"/><span class="lab"><font color="Green" title="E18">A7</font></span>: 
<font color="Maroon" title="c6">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D12" title="INCPROJ:def.12">INCPROJ:def 12</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">B</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E11:17"/><span class="lab"><font color="Green" title="E19">A8</font></span>: 
<font color="Maroon" title="c2">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">B</font>
 <span class="kw">and </span><br/><a NAME="E12:17"/><span class="lab"><font color="Green" title="E20">A9</font></span>: 
<font color="Maroon" title="c6">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">s</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E14:17"/><span class="lab"><font color="Green" title="E21">A10</font></span>: 
<font color="Maroon" title="c8">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">B</font>
 <span class="kw">and </span><br/><a NAME="E15:17"/><span class="lab"><font color="Green" title="E22">A11</font></span>: 
<font color="Maroon" title="c8">s</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">r</font>
 <span class="kw">and </span><br/><a NAME="E16:17"/><span class="lab"><font color="Green" title="E23">A12</font></span>: 
<font color="Maroon" title="c8">s</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="projred1.html#T8" target="_self" title="PROJRED1:th.8">Th8</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">L</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E18:17"/><span class="lab"><font color="Green" title="E24">A13</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L</font>
 <span class="kw">and </span><br/><a NAME="E19:17"/><span class="lab"><font color="Green" title="E25">A14</font></span>: 
<font color="Maroon" title="c8">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c10">Q</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E21:17"/><span class="lab"><font color="Green" title="E26">A15</font></span>: 
<font color="Maroon" title="c2">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">Q</font>
 <span class="kw">and </span><br/><a NAME="E22:17"/><span class="lab"><font color="Green" title="E27">A16</font></span>: 
<font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/>
<a NAME="E23:17"/><span class="lab"><font color="Green" title="E28">A17</font></span>: 
not <font color="Maroon" title="c4">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E22:17"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E24:17"/><span class="lab"><font color="Green" title="E29">A18</font></span>: 
not <font color="Maroon" title="c6">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E22:17"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E25:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A19</font></span>: 
not <font color="Maroon" title="c8">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="txt" href="#E15:17"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E26:17"/>
not <font color="Maroon" title="c6">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:17_1"/>
<font color="Maroon" title="c6">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:17_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="txt" href="#E16:17"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="txt" href="#E18:17"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="txt" href="#E19:17"><span class="lab"><font color="Green" title="E25">A14</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:17_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</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>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">a</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E28:17"/><span class="lab"><font color="Green" title="E31">A20</font></span>: 
<font color="Maroon" title="c11">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">Q</font>
 <span class="kw">and </span><br/><a NAME="E29:17"/><span class="lab"><font color="Green" title="E32">A21</font></span>: 
<font color="Maroon" title="c11">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E22:17"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="txt" href="#E18:17"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="txt" href="#E19:17"><span class="lab"><font color="Green" title="E25">A14</font></span></a>, <a class="txt" href="#E24:17"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="ref" href="incproj.html#D13" title="INCPROJ:def.13">INCPROJ:def 13</a></span>;<br/>
<a NAME="E30:17"/><span class="lab"><font color="Green" title="E33">A22</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c8">s</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">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:17"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="txt" href="#E19:17"><span class="lab"><font color="Green" title="E25">A14</font></span></a>, <a class="txt" href="#E29:17"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c12">R</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E32:17"/><span class="lab"><font color="Green" title="E34">A23</font></span>: 
<font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">R</font>
 <span class="kw">and </span><br/><a NAME="E33:17"/><span class="lab"><font color="Green" title="E35">A24</font></span>: 
<font color="Maroon" title="c8">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">R</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c13">S</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E35:17"/><span class="lab"><font color="Green" title="E36">A25</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">S</font>
 <span class="kw">and </span><br/><a NAME="E36:17"/><span class="lab"><font color="Green" title="E37">A26</font></span>: 
<font color="Maroon" title="c2">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/>
<a NAME="E37:17"/><span class="lab"><font color="Green" title="E38">A27</font></span>: 
not <font color="Maroon" title="c6">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E35:17"><span class="lab"><font color="Green" title="E36">A25</font></span></a>, <a class="txt" href="#E36:17"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E38:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A28</font></span>: 
not <font color="Maroon" title="c8">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="txt" href="#E15:17"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="txt" href="#E36:17"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E39:17"/><span class="lab"><font color="Green" title="E40">A29</font></span>: 
<font color="Maroon" title="c13">S</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="txt" href="#E15:17"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="txt" href="#E19:17"><span class="lab"><font color="Green" title="E25">A14</font></span></a>, <a class="txt" href="#E36:17"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="txt" href="#E37:17"><span class="lab"><font color="Green" title="E38">A27</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E40:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A30</font></span>: 
not <font color="Maroon" title="c2">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E18:17"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="txt" href="#E35:17"><span class="lab"><font color="Green" title="E36">A25</font></span></a>, <a class="txt" href="#E36:17"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E41:17"/><span class="lab"><font color="Green" title="E42">A31</font></span>: 
<font color="Maroon" title="c13">S</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E22:17"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="txt" href="#E35:17"><span class="lab"><font color="Green" title="E36">A25</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E42:17"/><span class="lab"><font color="Green" title="E43">A32</font></span>: 
not <font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E35:17"><span class="lab"><font color="Green" title="E36">A25</font></span></a>, <a class="txt" href="#E36:17"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E43:17"/><span class="lab"><font color="Green" title="E44">A33</font></span>: 
not <font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:17_2"/>
<font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:17_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E18:17"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="txt" href="#E19:17"><span class="lab"><font color="Green" title="E25">A14</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:17_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="txt" href="#E16:17"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</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="E44:17"/><span class="lab"><font color="Green" title="E45">A34</font></span>: 
not <font color="Maroon" title="c4">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">R</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:17_3"/>
<font color="Maroon" title="c4">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">R</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:17_3"/><span class="kw">then </span>
<font color="Maroon" title="c8">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E32:17"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="txt" href="#E33:17"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:17_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="txt" href="#E16:17"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</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="E45:17"/><span class="kw">then </span>
not <font color="Maroon" title="c6">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">R</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E32:17"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">b</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E47:17"/><span class="lab"><font color="Green" title="E46">A35</font></span>: 
<font color="Maroon" title="c14">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">R</font>
 <span class="kw">and </span><br/><a NAME="E48:17"/><span class="lab"><font color="Green" title="E47">A36</font></span>: 
<font color="Maroon" title="c14">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="txt" href="#E35:17"><span class="lab"><font color="Green" title="E36">A25</font></span></a>, <a class="txt" href="#E36:17"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="txt" href="#E32:17"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="txt" href="#E33:17"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="txt" href="#E37:17"><span class="lab"><font color="Green" title="E38">A27</font></span></a>, <a class="ref" href="incproj.html#D13" title="INCPROJ:def.13">INCPROJ:def 13</a></span>;<br/>
<a NAME="E49:17"/><span class="lab"><font color="Green" title="E48">A37</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c14">b</font>,<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c8">s</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="c12">R</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:17"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="txt" href="#E33:17"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="txt" href="#E47:17"><span class="lab"><font color="Green" title="E46">A35</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E50:17"/><span class="lab"><font color="Green" title="E49">A38</font></span>: 
<font color="Maroon" title="c12">R</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">Q</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:17_4"/>
not <font color="Maroon" title="c12">R</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">Q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:17_4"/><span class="kw">then </span>
<font color="Maroon" title="c7">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="txt" href="#E15:17"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E33:17"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:17_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E22:17"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</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="E51:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A39</font></span>: 
not <font color="Maroon" title="c2">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">R</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E22:17"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="txt" href="#E32:17"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E52:17"/><span class="lab"><font color="Green" title="E51">A40</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">c</font>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c8">s</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="c7">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E53:17"/><span class="lab"><font color="Green" title="E52">A41</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c14">b</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">r</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="c13">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:17"><span class="lab"><font color="Green" title="E36">A25</font></span></a>, <a class="txt" href="#E36:17"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="txt" href="#E48:17"><span class="lab"><font color="Green" title="E47">A36</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E54:17"/><span class="lab"><font color="Green" title="E53">A42</font></span>: 
<font color="Maroon" title="c11">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">r</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E18:17"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="txt" href="#E35:17"><span class="lab"><font color="Green" title="E36">A25</font></span></a>, <a class="txt" href="#E36:17"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="txt" href="#E29:17"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="txt" href="#E39:17"><span class="lab"><font color="Green" title="E40">A29</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E55:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A43</font></span>: 
not <font color="Maroon" title="c11">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E22:17"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="txt" href="#E36:17"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="txt" href="#E42:17"><span class="lab"><font color="Green" title="E43">A32</font></span></a>, <a class="txt" href="#E28:17"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E56:17"/><span class="lab"><font color="Green" title="E55">A44</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">r</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="c10">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E22:17"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="txt" href="#E28:17"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c15">C</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E58:17"/><span class="lab"><font color="Green" title="E56">A45</font></span>: 
<font color="Maroon" title="c11">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">C</font>
 <span class="kw">and </span><br/><a NAME="E59:17"/><span class="lab"><font color="Green" title="E57">A46</font></span>: 
<font color="Maroon" title="c14">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/>
<a NAME="E60:17"/>
<font color="Maroon" title="c11">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="txt" href="#E15:17"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E24:17"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="txt" href="#E28:17"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E61:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A47</font></span>: 
<font color="Maroon" title="c12">R</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:17"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="txt" href="#E19:17"><span class="lab"><font color="Green" title="E25">A14</font></span></a>, <a class="txt" href="#E33:17"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="txt" href="#E44:17"><span class="lab"><font color="Green" title="E45">A34</font></span></a>, <a class="txt" href="#E29:17"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="txt" href="#E58:17"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E62:17"/><span class="lab"><font color="Green" title="E59">A48</font></span>: 
not <font color="Maroon" title="c14">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:17"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="txt" href="#E32:17"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="txt" href="#E50:17"><span class="lab"><font color="Green" title="E49">A38</font></span></a>, <a class="txt" href="#E42:17"><span class="lab"><font color="Green" title="E43">A32</font></span></a>, <a class="txt" href="#E47:17"><span class="lab"><font color="Green" title="E46">A35</font></span></a>, <a class="txt" href="#E48:17"><span class="lab"><font color="Green" title="E47">A36</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E63:17"/><span class="kw">then </span>
not <font color="Maroon" title="c2">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E28:17"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="txt" href="#E58:17"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="txt" href="#E59:17"><span class="lab"><font color="Green" title="E57">A46</font></span></a>, <a class="txt" href="#E54:17"><span class="lab"><font color="Green" title="E53">A42</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c16">d</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E65:17"/><span class="lab"><font color="Green" title="E60">A49</font></span>: 
<font color="Maroon" title="c16">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">and </span><br/><a NAME="E66:17"/><span class="lab"><font color="Green" title="E61">A50</font></span>: 
<font color="Maroon" title="c16">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E22:17"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="txt" href="#E35:17"><span class="lab"><font color="Green" title="E36">A25</font></span></a>, <a class="txt" href="#E36:17"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="txt" href="#E28:17"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="txt" href="#E48:17"><span class="lab"><font color="Green" title="E47">A36</font></span></a>, <a class="txt" href="#E58:17"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="txt" href="#E59:17"><span class="lab"><font color="Green" title="E57">A46</font></span></a>, <a class="txt" href="#E41:17"><span class="lab"><font color="Green" title="E42">A31</font></span></a>, <a class="ref" href="incproj.html#D13" title="INCPROJ:def.13">INCPROJ:def 13</a></span>;<br/>
<a NAME="E67:17"/>
<font color="Maroon" title="c13">S</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E22:17"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="txt" href="#E36:17"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="txt" href="#E42:17"><span class="lab"><font color="Green" title="E43">A32</font></span></a>, <a class="txt" href="#E28:17"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="txt" href="#E58:17"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="txt" href="#E54:17"><span class="lab"><font color="Green" title="E53">A42</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E68:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A51</font></span>: 
<font color="Maroon" title="c16">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:17"><span class="lab"><font color="Green" title="E36">A25</font></span></a>, <a class="txt" href="#E44:17"><span class="lab"><font color="Green" title="E45">A34</font></span></a>, <a class="txt" href="#E47:17"><span class="lab"><font color="Green" title="E46">A35</font></span></a>, <a class="txt" href="#E48:17"><span class="lab"><font color="Green" title="E47">A36</font></span></a>, <a class="txt" href="#E59:17"><span class="lab"><font color="Green" title="E57">A46</font></span></a>, <a class="txt" href="#E66:17"><span class="lab"><font color="Green" title="E61">A50</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E69:17"/><span class="lab"><font color="Green" title="E63">A52</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">c</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</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="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E70:17"/><span class="lab"><font color="Green" title="E64">A53</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c14">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="c15">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E58:17"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="txt" href="#E59:17"><span class="lab"><font color="Green" title="E57">A46</font></span></a>, <a class="ref" href="incsp_1.html#T11" title="INCSP_1:th.11">INCSP_1:11</a></span>;<br/>
<a NAME="E71:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A54</font></span>: 
not <font color="Maroon" title="c6">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:17"><span class="lab"><font color="Green" title="E50">A39</font></span></a>, <a class="txt" href="#E23:17"><span class="lab"><font color="Green" title="E28">A17</font></span></a>, <a class="txt" href="#E42:17"><span class="lab"><font color="Green" title="E43">A32</font></span></a>, <a class="txt" href="#E43:17"><span class="lab"><font color="Green" title="E44">A33</font></span></a>, <a class="txt" href="#E44:17"><span class="lab"><font color="Green" title="E45">A34</font></span></a>, <a class="txt" href="#E25:17"><span class="lab"><font color="Green" title="E30">A19</font></span></a>, <a class="txt" href="#E40:17"><span class="lab"><font color="Green" title="E41">A30</font></span></a>, <a class="txt" href="#E38:17"><span class="lab"><font color="Green" title="E39">A28</font></span></a>, <a class="txt" href="#E30:17"><span class="lab"><font color="Green" title="E33">A22</font></span></a>, <a class="txt" href="#E56:17"><span class="lab"><font color="Green" title="E55">A44</font></span></a>, <a class="txt" href="#E49:17"><span class="lab"><font color="Green" title="E48">A37</font></span></a>, <a class="txt" href="#E53:17"><span class="lab"><font color="Green" title="E52">A41</font></span></a>, <a class="txt" href="#E69:17"><span class="lab"><font color="Green" title="E63">A52</font></span></a>, <a class="txt" href="#E52:17"><span class="lab"><font color="Green" title="E51">A40</font></span></a>, <a class="ref" href="incproj.html#D18" title="INCPROJ:def.18">INCPROJ:def 18</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c17">D</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E73:17"/><span class="lab"><font color="Green" title="E66">A55</font></span>: 
<font color="Maroon" title="c14">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">D</font>
 <span class="kw">and </span><br/><a NAME="E74:17"/><span class="lab"><font color="Green" title="E67">A56</font></span>: 
<font color="Maroon" title="c6">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">D</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/>
<a NAME="E75:17"/><span class="lab"><font color="Green" title="E68">A57</font></span>: 
<font color="Maroon" title="c12">R</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E32:17"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="txt" href="#E44:17"><span class="lab"><font color="Green" title="E45">A34</font></span></a>, <a class="txt" href="#E74:17"><span class="lab"><font color="Green" title="E67">A56</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E76:17"/>
<font color="Maroon" title="c16">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:17"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="txt" href="#E43:17"><span class="lab"><font color="Green" title="E44">A33</font></span></a>, <a class="txt" href="#E28:17"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="txt" href="#E29:17"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="txt" href="#E58:17"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="txt" href="#E59:17"><span class="lab"><font color="Green" title="E57">A46</font></span></a>, <a class="txt" href="#E62:17"><span class="lab"><font color="Green" title="E59">A48</font></span></a>, <a class="txt" href="#E66:17"><span class="lab"><font color="Green" title="E61">A50</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E77:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A58</font></span>: 
<font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c16">d</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_different</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E71:17"><span class="lab"><font color="Green" title="E65">A54</font></span></a>, <a class="txt" href="#E66:17"><span class="lab"><font color="Green" title="E61">A50</font></span></a>, <a class="txt" href="#E68:17"><span class="lab"><font color="Green" title="E62">A51</font></span></a>, <a class="ref" href="zfmisc_1.html#D6" title="ZFMISC_1:def.6">ZFMISC_1:def 6</a></span>;<br/>
<a NAME="E78:17"/>
<font color="Maroon" title="c13">S</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E35:17"><span class="lab"><font color="Green" title="E36">A25</font></span></a>, <a class="txt" href="#E36:17"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="txt" href="#E74:17"><span class="lab"><font color="Green" title="E67">A56</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E79:17"/><span class="kw">then </span>
<font color="Maroon" title="c15">C</font>,<font color="Maroon" title="c17">D</font>,<font color="Maroon" title="c12">R</font>,<font color="Maroon" title="c13">S</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_different</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:17"><span class="lab"><font color="Green" title="E36">A25</font></span></a>, <a class="txt" href="#E44:17"><span class="lab"><font color="Green" title="E45">A34</font></span></a>, <a class="txt" href="#E58:17"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="txt" href="#E71:17"><span class="lab"><font color="Green" title="E65">A54</font></span></a>, <a class="txt" href="#E74:17"><span class="lab"><font color="Green" title="E67">A56</font></span></a>, <a class="txt" href="#E55:17"><span class="lab"><font color="Green" title="E54">A43</font></span></a>, <a class="txt" href="#E75:17"><span class="lab"><font color="Green" title="E68">A57</font></span></a>, <a class="txt" href="#E61:17"><span class="lab"><font color="Green" title="E58">A47</font></span></a>, <a class="ref" href="zfmisc_1.html#D6" title="ZFMISC_1:def.6">ZFMISC_1:def 6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E80:17"/>
 ex <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r</font>, <font color="Olive" title="b4">s</font>, <font color="Olive" title="b5">a</font>, <font color="Olive" title="b6">b</font>, <font color="Olive" title="b7">c</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font> ex <font color="Olive" title="b8">A</font>, <font color="Olive" title="b9">B</font>, <font color="Olive" title="b10">C</font>, <font color="Olive" title="b11">Q</font>, <font color="Olive" title="b12">L</font>, <font color="Olive" title="b13">R</font>, <font color="Olive" title="b14">S</font>, <font color="Olive" title="b15">D</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> ex <font color="Olive" title="b16">d</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( not <font color="Olive" title="b2">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b12">L</font> &amp; not <font color="Olive" title="b3">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b12">L</font> &amp; not <font color="Olive" title="b1">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b11">Q</font> &amp; not <font color="Olive" title="b4">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b11">Q</font> &amp; not <font color="Olive" title="b1">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b13">R</font> &amp; not <font color="Olive" title="b3">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b13">R</font> &amp; not <font color="Olive" title="b2">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b14">S</font> &amp; not <font color="Olive" title="b4">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b14">S</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b5">a</font>,<font color="Olive" title="b1">p</font>,<font color="Olive" title="b4">s</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="Olive" title="b12">L</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b5">a</font>,<font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">r</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="Olive" title="b11">Q</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b6">b</font>,<font color="Olive" title="b2">q</font>,<font color="Olive" title="b4">s</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="Olive" title="b13">R</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b6">b</font>,<font color="Olive" title="b1">p</font>,<font color="Olive" title="b3">r</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="Olive" title="b14">S</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b7">c</font>,<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</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="Olive" title="b8">A</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b7">c</font>,<font color="Olive" title="b3">r</font>,<font color="Olive" title="b4">s</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="Olive" title="b9">B</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b5">a</font>,<font color="Olive" title="b6">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="Olive" title="b10">C</font> &amp; not <font color="Olive" title="b7">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b10">C</font> &amp; <font color="Olive" title="b6">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b15">D</font> &amp; <font color="Olive" title="b7">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b15">D</font> &amp; <font color="Olive" title="b10">C</font>,<font color="Olive" title="b15">D</font>,<font color="Olive" title="b13">R</font>,<font color="Olive" title="b14">S</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_different</a>  &amp; <font color="Olive" title="b16">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b8">A</font> &amp; <font color="Olive" title="b7">c</font>,<font color="Olive" title="b16">d</font>,<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_different</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:17"><span class="lab"><font color="Green" title="E50">A39</font></span></a>, <a class="txt" href="#E23:17"><span class="lab"><font color="Green" title="E28">A17</font></span></a>, <a class="txt" href="#E42:17"><span class="lab"><font color="Green" title="E43">A32</font></span></a>, <a class="txt" href="#E43:17"><span class="lab"><font color="Green" title="E44">A33</font></span></a>, <a class="txt" href="#E44:17"><span class="lab"><font color="Green" title="E45">A34</font></span></a>, <a class="txt" href="#E25:17"><span class="lab"><font color="Green" title="E30">A19</font></span></a>, <a class="txt" href="#E40:17"><span class="lab"><font color="Green" title="E41">A30</font></span></a>, <a class="txt" href="#E38:17"><span class="lab"><font color="Green" title="E39">A28</font></span></a>, <a class="txt" href="#E30:17"><span class="lab"><font color="Green" title="E33">A22</font></span></a>, <a class="txt" href="#E56:17"><span class="lab"><font color="Green" title="E55">A44</font></span></a>, <a class="txt" href="#E49:17"><span class="lab"><font color="Green" title="E48">A37</font></span></a>, <a class="txt" href="#E53:17"><span class="lab"><font color="Green" title="E52">A41</font></span></a>, <a class="txt" href="#E69:17"><span class="lab"><font color="Green" title="E63">A52</font></span></a>, <a class="txt" href="#E52:17"><span class="lab"><font color="Green" title="E51">A40</font></span></a>, <a class="txt" href="#E70:17"><span class="lab"><font color="Green" title="E64">A53</font></span></a>, <a class="txt" href="#E71:17"><span class="lab"><font color="Green" title="E65">A54</font></span></a>, <a class="txt" href="#E73:17"><span class="lab"><font color="Green" title="E66">A55</font></span></a>, <a class="txt" href="#E74:17"><span class="lab"><font color="Green" title="E67">A56</font></span></a>, <a class="txt" href="#E65:17"><span class="lab"><font color="Green" title="E60">A49</font></span></a>, <a class="txt" href="#E77:17"><span class="lab"><font color="Green" title="E69">A58</font></span></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>
