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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be    <a href="incsp_1.html#L1" title="INCSP_1:struct.1">IncProjStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font> being   <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/> for <font color="Olive" title="b2">K</font> being  <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>  st <font color="Olive" title="b1">F</font> is  <a href="combgras.html#V6" title="COMBGRAS:attr.6">incidence_preserving</a>  &amp; <font color="Olive" title="b2">K</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a>  holds <br/><font color="Olive" title="b1">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Olive" title="b2">K</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a> </span><br/><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">K</font> being  <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>  st <font color="Maroon" title="c2">F</font> is  <a href="combgras.html#V6" title="COMBGRAS:attr.6">incidence_preserving</a>  &amp; <font color="Olive" title="b1">K</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a>  holds <br/><font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Olive" title="b1">K</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a> </span><br/><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">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>  implies <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a>  )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:35"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
<font color="Maroon" title="c2">F</font> is  <a href="combgras.html#V6" title="COMBGRAS:attr.6">incidence_preserving</a> 
 <span class="kw">and </span><br/><a NAME="E2:35"/><span class="lab"><font color="Green" title="E27">A2</font></span>: 
<font color="Maroon" title="c3">K</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a> </span><br/>

<span class="kw">let </span><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>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="combgras.html#D2" target="_self" title="COMBGRAS:def.2">COMBGRAS:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="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> implies  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> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E3:35"/><span class="lab"><font color="Green" title="E28">A3</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E4:35"/><span class="lab"><font color="Green" title="E29">A4</font></span>: 
<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>
 ; <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">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></span><br/>

<a NAME="E5:35"/><span class="lab"><font color="Green" title="E30">A5</font></span>: 
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="combgras.html#T18" target="_self" title="COMBGRAS:th.18">Th18</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E7:35"/><span class="lab"><font color="Green" title="E31">A6</font></span>: 
<font color="Maroon" title="c4">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">B11</font>
 <span class="kw">and </span><br/><a NAME="E8:35"/><span class="lab"><font color="Green" title="E32">A7</font></span>: 
 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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35"><span class="lab"><font color="Green" title="E28">A3</font></span></a></span>;<br/>
<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E10:35"/><span class="lab"><font color="Green" title="E33">A8</font></span>: 
<font color="Maroon" title="c5">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">B12</font>
 <span class="kw">and </span><br/><a NAME="E11:35"/><span class="lab"><font color="Green" title="E34">A9</font></span>: 
 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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:35"><span class="lab"><font color="Green" title="E30">A5</font></span></a>, <a class="txt" href="#E4:35"><span class="lab"><font color="Green" title="E29">A4</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">A12</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="E13:35"/><span class="lab"><font color="Green" title="E35">A10</font></span>: 
<font color="Maroon" title="c8">A12</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font>
 <span class="kw">and </span><br/><a NAME="E14:35"/><span class="lab"><font color="Green" title="E36">A11</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="combgras.html#K2" title="COMBGRAS:func.2">.</a> <font color="Maroon" title="c8">A12</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">B12</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:35"><span class="lab"><font color="Green" title="E34">A9</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">A11</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="E16:35"/><span class="lab"><font color="Green" title="E37">A12</font></span>: 
<font color="Maroon" title="c9">A11</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font>
 <span class="kw">and </span><br/><a NAME="E17:35"/><span class="lab"><font color="Green" title="E38">A13</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="combgras.html#K2" title="COMBGRAS:func.2">.</a> <font color="Maroon" title="c9">A11</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">B11</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:35"><span class="lab"><font color="Green" title="E32">A7</font></span></a></span>;<br/>
<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E19:35"/><span class="lab"><font color="Green" title="E39">A14</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c9">A11</font>,<font color="Maroon" title="c8">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="txt" href="#E16:35"><span class="lab"><font color="Green" title="E37">A12</font></span></a>, <a class="txt" href="#E13:35"><span class="lab"><font color="Green" title="E35">A10</font></span></a>, <a class="ref" href="combgras.html#D2" target="_self" title="COMBGRAS:def.2">Def2</a></span>;<br/>
<a NAME="E20:35"/>
<font color="Maroon" title="c8">A12</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">L1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:35"><span class="lab"><font color="Green" title="E39">A14</font></span></a>, <a class="ref" href="incsp_1.html#T11" title="INCSP_1:th.11">INCSP_1:11</a></span>;<br/>
<a NAME="E21:35"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A15</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="combgras.html#K2" title="COMBGRAS:func.2">.</a> <font color="Maroon" title="c8">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="combgras.html#D8" target="_self" title="COMBGRAS:def.8">Def8</a></span>;<br/>
<a NAME="E22:35"/>
<font color="Maroon" title="c9">A11</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">L1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:35"><span class="lab"><font color="Green" title="E39">A14</font></span></a>, <a class="ref" href="incsp_1.html#T11" title="INCSP_1:th.11">INCSP_1:11</a></span>;<br/>
<a NAME="E23:35"/><span class="kw">then </span>
<font color="Maroon" title="c2">F</font> <a href="combgras.html#K2" title="COMBGRAS:func.2">.</a> <font color="Maroon" title="c9">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="combgras.html#D8" target="_self" title="COMBGRAS:def.8">Def8</a></span>;<br/>
<a NAME="E24:35"/><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="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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:35"><span class="lab"><font color="Green" title="E31">A6</font></span></a>, <a class="txt" href="#E10:35"><span class="lab"><font color="Green" title="E33">A8</font></span></a>, <a class="txt" href="#E17:35"><span class="lab"><font color="Green" title="E38">A13</font></span></a>, <a class="txt" href="#E14:35"><span class="lab"><font color="Green" title="E36">A11</font></span></a>, <a class="txt" href="#E21:35"><span class="lab"><font color="Green" title="E40">A15</font></span></a>, <a class="ref" href="incsp_1.html#T11" title="INCSP_1:th.11">INCSP_1:11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E25:35"/>
 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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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