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<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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">L1</font>, <font color="Olive" title="b2">L2</font>, <font color="Olive" title="b3">L</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b4">P</font> being   <a href="incsp_1.html#NM3" title="INCSP_1:NM.3">PLANE</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">L1</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b4">P</font> &amp; <font color="Olive" title="b2">L2</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b4">P</font> &amp;  not <font color="Olive" title="b3">L</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b4">P</font> &amp; <font color="Olive" title="b1">L1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">L2</font> holds <br/> for <font color="Olive" title="b5">Q</font> being   <a href="incsp_1.html#NM3" title="INCSP_1:NM.3">PLANE</a> of <font color="Maroon" title="c1">S</font>  holds <br/>(  not <font color="Olive" title="b3">L</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b5">Q</font> or  not <font color="Olive" title="b1">L1</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b5">Q</font> or  not <font color="Olive" title="b2">L2</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b5">Q</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">L1</font>, <font color="Maroon" title="c3">L2</font>, <font color="Maroon" title="c4">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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">P</font> being   <a href="incsp_1.html#NM3" title="INCSP_1:NM.3">PLANE</a> of <font color="Maroon" title="c1">S</font>  st <font color="Maroon" title="c2">L1</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b1">P</font> &amp; <font color="Maroon" title="c3">L2</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b1">P</font> &amp;  not <font color="Maroon" title="c4">L</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b1">P</font> &amp; <font color="Maroon" title="c2">L1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">L2</font> holds <br/> for <font color="Olive" title="b2">Q</font> being   <a href="incsp_1.html#NM3" title="INCSP_1:NM.3">PLANE</a> of <font color="Maroon" title="c1">S</font>  holds <br/>(  not <font color="Maroon" title="c4">L</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b2">Q</font> or  not <font color="Maroon" title="c2">L1</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b2">Q</font> or  not <font color="Maroon" title="c3">L2</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b2">Q</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">P</font> be   <a href="incsp_1.html#NM3" title="INCSP_1:NM.3">PLANE</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">L1</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c5">P</font> &amp; <font color="Maroon" title="c3">L2</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c5">P</font> &amp;  not <font color="Maroon" title="c4">L</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c5">P</font> &amp; <font color="Maroon" title="c2">L1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">L2</font> implies  for <font color="Olive" title="b1">Q</font> being   <a href="incsp_1.html#NM3" title="INCSP_1:NM.3">PLANE</a> of <font color="Maroon" title="c1">S</font>  holds <br/>(  not <font color="Maroon" title="c4">L</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b1">Q</font> or  not <font color="Maroon" title="c2">L1</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b1">Q</font> or  not <font color="Maroon" title="c3">L2</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b1">Q</font> ) )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:40"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
<font color="Maroon" title="c2">L1</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c5">P</font>
 <span class="kw">and </span><br/><a NAME="E2:40"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
<font color="Maroon" title="c3">L2</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c5">P</font>
 <span class="kw">and </span><br/><a NAME="E3:40"/><span class="lab"><font color="Green" title="E39">A3</font></span>: 
 not <font color="Maroon" title="c4">L</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c5">P</font>
 <span class="kw">and </span><br/><a NAME="E4:40"/><span class="lab"><font color="Green" title="E40">A4</font></span>: 
<font color="Maroon" title="c2">L1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">L2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Q</font> being   <a href="incsp_1.html#NM3" title="INCSP_1:NM.3">PLANE</a> of <font color="Maroon" title="c1">S</font>  holds <br/>(  not <font color="Maroon" title="c4">L</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b1">Q</font> or  not <font color="Maroon" title="c2">L1</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b1">Q</font> or  not <font color="Maroon" title="c3">L2</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Olive" title="b1">Q</font> )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c6">A</font>, <font color="Maroon" title="c7">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="E6:40"/><span class="lab"><font color="Green" title="E41">A5</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">B</font>
 <span class="kw">and </span><br/><a NAME="E7:40"/><span class="lab"><font color="Green" title="E42">A6</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">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">L1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incsp_1.html#D8" target="_self" title="INCSP_1:def.8">Def8</a></span>;<br/>
<a NAME="E8:40"/><span class="lab"><font color="Green" title="E43">A7</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">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:40"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="txt" href="#E7:40"><span class="lab"><font color="Green" title="E42">A6</font></span></a>, <a class="ref" href="incsp_1.html#T14" target="_self" title="INCSP_1:th.14">Th35</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">C</font>, <font color="Maroon" title="c9">C1</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="E10:40"/><span class="lab"><font color="Green" title="E44">A8</font></span>: 
<font color="Maroon" title="c8">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">C1</font>
 <span class="kw">and </span><br/><a NAME="E11:40"/><span class="lab"><font color="Green" title="E45">A9</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c8">C</font>,<font color="Maroon" title="c9">C1</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">L2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incsp_1.html#D8" target="_self" title="INCSP_1:def.8">Def8</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E46">A10</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="40_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:40_1"/>
( <font color="Maroon" title="c8">C</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">L1</font> &amp; <font color="Maroon" title="c9">C1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">L1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:40_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="c8">C</font>,<font color="Maroon" title="c9">C1</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">L1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incsp_1.html#T1" target="_self" title="INCSP_1:th.1">Th11</a></span>;<br/><span class="kw">hence </span><a NAME="E3:40_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:40"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="txt" href="#E10:40"><span class="lab"><font color="Green" title="E44">A8</font></span></a>, <a class="txt" href="#E11:40"><span class="lab"><font color="Green" title="E45">A9</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="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E13:40"/><span class="lab"><font color="Green" title="E47">A11</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c8">C</font>,<font color="Maroon" title="c9">C1</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:40"><span class="lab"><font color="Green" title="E38">A2</font></span></a>, <a class="txt" href="#E11:40"><span class="lab"><font color="Green" title="E45">A9</font></span></a>, <a class="ref" href="incsp_1.html#T14" target="_self" title="INCSP_1:th.14">Th35</a></span>;<br/>
<a NAME="E14:40"/><span class="kw">then </span>
<font color="Maroon" title="c8">C</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="incsp_1.html#T3" target="_self" title="INCSP_1:th.3">Th13</a></span>;<br/>
<a NAME="E15:40"/><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="c7">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">C</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:40"><span class="lab"><font color="Green" title="E43">A7</font></span></a>, <a class="ref" href="incsp_1.html#T9" target="_self" title="INCSP_1:th.9">Th19</a></span>;<br/>
<a NAME="E16:40"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A12</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="c7">B</font>,<font color="Maroon" title="c8">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> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T3" title="ENUMSET1:th.3">ENUMSET1:3</a></span>;<br/>
<a NAME="E17:40"/>
<font color="Maroon" title="c9">C1</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:40"><span class="lab"><font color="Green" title="E47">A11</font></span></a>, <a class="ref" href="incsp_1.html#T3" target="_self" title="INCSP_1:th.3">Th13</a></span>;<br/>
<a NAME="E18:40"/><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="c7">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c9">C1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:40"><span class="lab"><font color="Green" title="E43">A7</font></span></a>, <a class="ref" href="incsp_1.html#T9" target="_self" title="INCSP_1:th.9">Th19</a></span>;<br/>
<a NAME="E19:40"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">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="c7">B</font>,<font color="Maroon" title="c9">C1</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> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T3" title="ENUMSET1:th.3">ENUMSET1:3</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c10">D</font>, <font color="Maroon" title="c11">E</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="E21:40"/><span class="lab"><font color="Green" title="E50">A14</font></span>: 
<font color="Maroon" title="c10">D</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">E</font>
 <span class="kw">and </span><br/><a NAME="E22:40"/><span class="lab"><font color="Green" title="E51">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="c10">D</font>,<font color="Maroon" title="c11">E</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="c4">L</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incsp_1.html#D8" target="_self" title="INCSP_1:def.8">Def8</a></span>;<br/>
<span class="kw">given </span><font color="Maroon" title="c12">Q</font> being   <a href="incsp_1.html#NM3" title="INCSP_1:NM.3">PLANE</a> of <font color="Maroon" title="c1">S</font><span class="kw"> such that </span><a NAME="E24:40"/><span class="lab"><font color="Green" title="E52">A16</font></span>: 
<font color="Maroon" title="c4">L</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c12">Q</font>
 <span class="kw">and </span><br/><a NAME="E25:40"/><span class="lab"><font color="Green" title="E53">A17</font></span>: 
<font color="Maroon" title="c2">L1</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c12">Q</font>
 <span class="kw">and </span><br/><a NAME="E26:40"/><span class="lab"><font color="Green" title="E54">A18</font></span>: 
<font color="Maroon" title="c3">L2</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c12">Q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E27:40"/><span class="lab"><font color="Green" title="E55">A19</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">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:40"><span class="lab"><font color="Green" title="E53">A17</font></span></a>, <a class="txt" href="#E7:40"><span class="lab"><font color="Green" title="E42">A6</font></span></a>, <a class="ref" href="incsp_1.html#T14" target="_self" title="INCSP_1:th.14">Th35</a></span>;<br/>
<a NAME="E28:40"/><span class="lab"><font color="Green" title="E56">A20</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c8">C</font>,<font color="Maroon" title="c9">C1</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:40"><span class="lab"><font color="Green" title="E54">A18</font></span></a>, <a class="txt" href="#E11:40"><span class="lab"><font color="Green" title="E45">A9</font></span></a>, <a class="ref" href="incsp_1.html#T14" target="_self" title="INCSP_1:th.14">Th35</a></span>;<br/>
<a NAME="E29:40"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A21</font></span>: 
<font color="Maroon" title="c8">C</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="incsp_1.html#T3" target="_self" title="INCSP_1:th.3">Th13</a></span>;<br/>
<a NAME="E30:40"/><span class="lab"><font color="Green" title="E58">A22</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c10">D</font>,<font color="Maroon" title="c11">E</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:40"><span class="lab"><font color="Green" title="E52">A16</font></span></a>, <a class="txt" href="#E22:40"><span class="lab"><font color="Green" title="E51">A15</font></span></a>, <a class="ref" href="incsp_1.html#T14" target="_self" title="INCSP_1:th.14">Th35</a></span>;<br/>
<a NAME="E31:40"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A23</font></span>: 
<font color="Maroon" title="c10">D</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="incsp_1.html#T3" target="_self" title="INCSP_1:th.3">Th13</a></span>;<br/>
<a NAME="E32:40"/><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="c8">C</font>,<font color="Maroon" title="c10">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:40"><span class="lab"><font color="Green" title="E57">A21</font></span></a>, <a class="ref" href="incsp_1.html#T3" target="_self" title="INCSP_1:th.3">Th13</a></span>;<br/>
<a NAME="E33:40"/><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="c7">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c8">C</font>,<font color="Maroon" title="c10">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:40"><span class="lab"><font color="Green" title="E55">A19</font></span></a>, <a class="ref" href="incsp_1.html#T11" target="_self" title="INCSP_1:th.11">Th21</a></span>;<br/>
<a NAME="E34:40"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">B</font>,<font color="Maroon" title="c8">C</font>,<font color="Maroon" title="c10">D</font></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T5" title="ENUMSET1:th.5">ENUMSET1:5</a></span>;<br/>
<a NAME="E35:40"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A24</font></span>: 
<span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">B</font>,<font color="Maroon" title="c8">C</font>,<font color="Maroon" title="c10">D</font></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span> is  <a href="incsp_1.html#V4" title="INCSP_1:attr.4">planar</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="incsp_1.html#D7" target="_self" title="INCSP_1:def.7">Def7</a></span>;<br/>
<a NAME="E36:40"/><span class="lab"><font color="Green" title="E61">A25</font></span>: 
<font color="Maroon" title="c11">E</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:40"><span class="lab"><font color="Green" title="E58">A22</font></span></a>, <a class="ref" href="incsp_1.html#T3" target="_self" title="INCSP_1:th.3">Th13</a></span>;<br/>
<a NAME="E37:40"/><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="c8">C</font>,<font color="Maroon" title="c11">E</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:40"><span class="lab"><font color="Green" title="E57">A21</font></span></a>, <a class="ref" href="incsp_1.html#T3" target="_self" title="INCSP_1:th.3">Th13</a></span>;<br/>
<a NAME="E38:40"/><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="c7">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c8">C</font>,<font color="Maroon" title="c11">E</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:40"><span class="lab"><font color="Green" title="E55">A19</font></span></a>, <a class="ref" href="incsp_1.html#T11" target="_self" title="INCSP_1:th.11">Th21</a></span>;<br/>
<a NAME="E39:40"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">B</font>,<font color="Maroon" title="c8">C</font>,<font color="Maroon" title="c11">E</font></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T5" title="ENUMSET1:th.5">ENUMSET1:5</a></span>;<br/>
<a NAME="E40:40"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A26</font></span>: 
<span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">B</font>,<font color="Maroon" title="c8">C</font>,<font color="Maroon" title="c11">E</font></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span> is  <a href="incsp_1.html#V4" title="INCSP_1:attr.4">planar</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="incsp_1.html#D7" target="_self" title="INCSP_1:def.7">Def7</a></span>;<br/>
<a NAME="E41:40"/><span class="lab"><font color="Green" title="E63">A27</font></span>: 
<font color="Maroon" title="c9">C1</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:40"><span class="lab"><font color="Green" title="E56">A20</font></span></a>, <a class="ref" href="incsp_1.html#T3" target="_self" title="INCSP_1:th.3">Th13</a></span>;<br/>
<a NAME="E42:40"/><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="c9">C1</font>,<font color="Maroon" title="c10">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:40"><span class="lab"><font color="Green" title="E59">A23</font></span></a>, <a class="ref" href="incsp_1.html#T3" target="_self" title="INCSP_1:th.3">Th13</a></span>;<br/>
<a NAME="E43:40"/><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="c7">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c9">C1</font>,<font color="Maroon" title="c10">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:40"><span class="lab"><font color="Green" title="E55">A19</font></span></a>, <a class="ref" href="incsp_1.html#T11" target="_self" title="INCSP_1:th.11">Th21</a></span>;<br/>
<a NAME="E44:40"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">B</font>,<font color="Maroon" title="c9">C1</font>,<font color="Maroon" title="c10">D</font></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T5" title="ENUMSET1:th.5">ENUMSET1:5</a></span>;<br/>
<a NAME="E45:40"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A28</font></span>: 
<span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">B</font>,<font color="Maroon" title="c9">C1</font>,<font color="Maroon" title="c10">D</font></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span> is  <a href="incsp_1.html#V4" title="INCSP_1:attr.4">planar</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="incsp_1.html#D7" target="_self" title="INCSP_1:def.7">Def7</a></span>;<br/>
<a NAME="E46:40"/>
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c9">C1</font>,<font color="Maroon" title="c11">E</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:40"><span class="lab"><font color="Green" title="E63">A27</font></span></a>, <a class="txt" href="#E36:40"><span class="lab"><font color="Green" title="E61">A25</font></span></a>, <a class="ref" href="incsp_1.html#T3" target="_self" title="INCSP_1:th.3">Th13</a></span>;<br/>
<a NAME="E47:40"/><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="c7">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c9">C1</font>,<font color="Maroon" title="c11">E</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:40"><span class="lab"><font color="Green" title="E55">A19</font></span></a>, <a class="ref" href="incsp_1.html#T11" target="_self" title="INCSP_1:th.11">Th21</a></span>;<br/>
<a NAME="E48:40"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">B</font>,<font color="Maroon" title="c9">C1</font>,<font color="Maroon" title="c11">E</font></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c12">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T5" title="ENUMSET1:th.5">ENUMSET1:5</a></span>;<br/>
<a NAME="E49:40"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A29</font></span>: 
<span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">B</font>,<font color="Maroon" title="c9">C1</font>,<font color="Maroon" title="c11">E</font></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span> is  <a href="incsp_1.html#V4" title="INCSP_1:attr.4">planar</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="incsp_1.html#D7" target="_self" title="INCSP_1:def.7">Def7</a></span>;<br/>
<a NAME="E50:40"/>
 not <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c10">D</font>,<font color="Maroon" title="c11">E</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:40"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="txt" href="#E21:40"><span class="lab"><font color="Green" title="E50">A14</font></span></a>, <a class="txt" href="#E22:40"><span class="lab"><font color="Green" title="E51">A15</font></span></a>, <a class="ref" href="incsp_1.html#D14" target="_self" title="INCSP_1:def.14">Def14</a></span>;<br/>
<a NAME="E51:40"/><span class="kw">then </span>
(  not <font color="Maroon" title="c10">D</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a> <font color="Maroon" title="c5">P</font> or  not <font color="Maroon" title="c11">E</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a> <font color="Maroon" title="c5">P</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="incsp_1.html#T3" target="_self" title="INCSP_1:th.3">Th13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E52:40"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:40"><span class="lab"><font color="Green" title="E41">A5</font></span></a>, <a class="txt" href="#E7:40"><span class="lab"><font color="Green" title="E42">A6</font></span></a>, <a class="txt" href="#E35:40"><span class="lab"><font color="Green" title="E60">A24</font></span></a>, <a class="txt" href="#E40:40"><span class="lab"><font color="Green" title="E62">A26</font></span></a>, <a class="txt" href="#E45:40"><span class="lab"><font color="Green" title="E64">A28</font></span></a>, <a class="txt" href="#E49:40"><span class="lab"><font color="Green" title="E65">A29</font></span></a>, <a class="txt" href="#E12:40"><span class="lab"><font color="Green" title="E46">A10</font></span></a>, <a class="txt" href="#E16:40"><span class="lab"><font color="Green" title="E48">A12</font></span></a>, <a class="txt" href="#E19:40"><span class="lab"><font color="Green" title="E49">A13</font></span></a>, <a class="ref" href="incsp_1.html#T18" target="_self" title="INCSP_1:th.18">Th39</a>, <a class="ref" href="incsp_1.html#T19" target="_self" title="INCSP_1:th.19">Th40</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
