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<b>let </b><font color="Maroon" title="c1">S</font> be    <a href="incsp_1.html#L1" title="INCSP_1:struct.1">IncProjStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">F</font> be    <a href="combgras.html#L1" title="COMBGRAS:struct.1">IncProjMap</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c3">K</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">S</font>;<br/>





<b>assume </b><a NAME="E1:35"/><i><font color="Green" title="E26">A1</font></i>: 
( <font color="Maroon" title="c2">F</font> is <a href="combgras.html#V6" title="COMBGRAS:attr.6">incidence_preserving</a> &amp; <font color="Maroon" title="c3">K</font> is <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a> )
 ;<br/>

<a NAME="E2:35"/><i><font color="Green" title="E27">A2</font></i>: 
<font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">B</font> where <font color="Olive" title="b1">B</font> is   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font> :  ex <font color="Olive" title="b2">A</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Olive" title="b2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c2">F</font> <a href="combgras.html#K2" title="COMBGRAS:func.2">.</a> <font color="Olive" title="b2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">B</font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="combgras.html#T18" target="_self" title="COMBGRAS:th.18">Th18</a></i>;<br/>
<b>let </b><font color="Maroon" title="c4">B1</font>, <font color="Maroon" title="c5">B2</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="combgras.html#D2" target="_self" title="COMBGRAS:def.2">COMBGRAS:def 2</a><br/>

<b>assume </b><a NAME="E3:35"/><i><font color="Green" title="E28">A3</font></i>: 
( <font color="Maroon" title="c4">B1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c5">B2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font> )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c6">B11</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E5:35"/><i><font color="Green" title="E29">A4</font></i>: 
( <font color="Maroon" title="c4">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">B11</font> &amp;  ex <font color="Olive" title="b1">A</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c2">F</font> <a href="combgras.html#K2" title="COMBGRAS:func.2">.</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">B11</font> ) )
 <b>by </b><i><a class="txt" href="combgras.html#E2:35"><i><font color="Green" title="E27">A2</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">B12</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E7:35"/><i><font color="Green" title="E30">A5</font></i>: 
( <font color="Maroon" title="c5">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">B12</font> &amp;  ex <font color="Olive" title="b1">A</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c2">F</font> <a href="combgras.html#K2" title="COMBGRAS:func.2">.</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">B12</font> ) )
 <b>by </b><i><a class="txt" href="combgras.html#E2:35"><i><font color="Green" title="E27">A2</font></i></a>, <a class="txt" href="combgras.html#E3:35"><i><font color="Green" title="E28">A3</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">A11</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E9:35"/><i><font color="Green" title="E31">A6</font></i>: 
( <font color="Maroon" title="c8">A11</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c2">F</font> <a href="combgras.html#K2" title="COMBGRAS:func.2">.</a> <font color="Maroon" title="c8">A11</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">B11</font> )
 <b>by </b><i><a class="txt" href="combgras.html#E5:35"><i><font color="Green" title="E29">A4</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">A12</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E11:35"/><i><font color="Green" title="E32">A7</font></i>: 
( <font color="Maroon" title="c9">A12</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c2">F</font> <a href="combgras.html#K2" title="COMBGRAS:func.2">.</a> <font color="Maroon" title="c9">A12</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">B12</font> )
 <b>by </b><i><a class="txt" href="combgras.html#E7:35"><i><font color="Green" title="E30">A5</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">L1</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E13:35"/><i><font color="Green" title="E33">A8</font></i>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c8">A11</font>,<font color="Maroon" title="c9">A12</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="c10">L1</font>
 <b>by </b><i><a class="txt" href="combgras.html#E1:35"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="combgras.html#E9:35"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="combgras.html#E11:35"><i><font color="Green" title="E32">A7</font></i></a>, <a class="ref" href="combgras.html#D2" target="_self" title="COMBGRAS:def.2">Def2</a></i>;<br/>
<a NAME="E14:35"/>
( <font color="Maroon" title="c8">A11</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">L1</font> &amp; <font color="Maroon" title="c9">A12</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">L1</font> )
 
<b>by </b><i><a class="txt" href="combgras.html#E13:35"><i><font color="Green" title="E33">A8</font></i></a>, <a class="ref" href="incsp_1.html#T11" title="INCSP_1:th.11">INCSP_1:11</a></i>;<br/>
<a NAME="E15:35"/><b>then </b>
( <font color="Maroon" title="c2">F</font> <a href="combgras.html#K2" title="COMBGRAS:func.2">.</a> <font color="Maroon" title="c8">A11</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K3" title="COMBGRAS:func.3">.</a> <font color="Maroon" title="c10">L1</font> &amp; <font color="Maroon" title="c2">F</font> <a href="combgras.html#K2" title="COMBGRAS:func.2">.</a> <font color="Maroon" title="c9">A12</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K3" title="COMBGRAS:func.3">.</a> <font color="Maroon" title="c10">L1</font> )
 
<b>by </b><i><a class="txt" href="combgras.html#E1:35"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="combgras.html#D8" target="_self" title="COMBGRAS:def.8">Def8</a></i>;<br/>
<a NAME="E16:35"/><b>then </b>
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">B1</font>,<font color="Maroon" title="c5">B2</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">F</font> <a href="combgras.html#K3" title="COMBGRAS:func.3">.</a> <font color="Maroon" title="c10">L1</font>
 
<b>by </b><i><a class="txt" href="combgras.html#E5:35"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="combgras.html#E7:35"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="combgras.html#E9:35"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="combgras.html#E11:35"><i><font color="Green" title="E32">A7</font></i></a>, <a class="ref" href="incsp_1.html#T11" title="INCSP_1:th.11">INCSP_1:11</a></i>;<br/>
<b>hence </b><a NAME="E17:35"/>
 ex <font color="Olive" title="b1">L</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">S</font> st <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">B1</font>,<font color="Maroon" title="c5">B2</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="b1">L</font>
 ;<br/>


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