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<span class="kw">let </span><font color="Maroon" title="c1">G</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">b1</font>, <font color="Olive" title="b4">b2</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font><br/>  for <font color="Olive" title="b5">A</font>, <font color="Olive" title="b6">B</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">G</font>  st <font color="Maroon" title="c1">G</font> is  <a href="projpl_1.html#V1" title="PROJPL_1:attr.1">configuration</a>  &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">a2</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="b5">A</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">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="b6">B</font> &amp; <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">a2</font> <a href="projpl_1.html#R1" title="PROJPL_1:pred.1">|'</a> <font color="Olive" title="b6">B</font> &amp; <font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">b2</font> <a href="projpl_1.html#R1" title="PROJPL_1:pred.1">|'</a> <font color="Olive" title="b5">A</font> &amp; <font color="Olive" title="b1">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">a2</font> &amp; <font color="Olive" title="b3">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">b2</font> holds <br/><font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">a2</font>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">b2</font> <a href="projpl_1.html#R5" title="PROJPL_1:pred.5">is_a_quadrangle</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">a2</font>, <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">G</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">A</font>, <font color="Olive" title="b2">B</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">G</font>  st <font color="Maroon" title="c1">G</font> is  <a href="projpl_1.html#V1" title="PROJPL_1:attr.1">configuration</a>  &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</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">A</font> &amp; <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="b2">B</font> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="projpl_1.html#R1" title="PROJPL_1:pred.1">|'</a> <font color="Olive" title="b2">B</font> &amp; <font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font> <a href="projpl_1.html#R1" title="PROJPL_1:pred.1">|'</a> <font color="Olive" title="b1">A</font> &amp; <font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a2</font> &amp; <font color="Maroon" title="c4">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> holds <br/><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font> <a href="projpl_1.html#R5" title="PROJPL_1:pred.5">is_a_quadrangle</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c6">A</font>, <font color="Maroon" title="c7">B</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">G</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="c1">G</font> is  <a href="projpl_1.html#V1" title="PROJPL_1:attr.1">configuration</a>  &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</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="c6">A</font> &amp; <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="c7">B</font> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="projpl_1.html#R1" title="PROJPL_1:pred.1">|'</a> <font color="Maroon" title="c7">B</font> &amp; <font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font> <a href="projpl_1.html#R1" title="PROJPL_1:pred.1">|'</a> <font color="Maroon" title="c6">A</font> &amp; <font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a2</font> &amp; <font color="Maroon" title="c4">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> implies <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font> <a href="projpl_1.html#R5" title="PROJPL_1:pred.5">is_a_quadrangle</a>  )</span><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:21"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
<font color="Maroon" title="c1">G</font> is  <a href="projpl_1.html#V1" title="PROJPL_1:attr.1">configuration</a> 
 <span class="kw">and </span><br/><a NAME="E2:21"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</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="c6">A</font>
 <span class="kw">and </span><br/><a NAME="E3:21"/><span class="lab"><font color="Green" title="E21">A3</font></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="c7">B</font>
 <span class="kw">and </span><br/><a NAME="E4:21"/><span class="lab"><font color="Green" title="E22">A4</font></span>: 
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="projpl_1.html#R1" title="PROJPL_1:pred.1">|'</a> <font color="Maroon" title="c7">B</font>
 <span class="kw">and </span><br/><a NAME="E5:21"/><span class="lab"><font color="Green" title="E23">A5</font></span>: 
<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font> <a href="projpl_1.html#R1" title="PROJPL_1:pred.1">|'</a> <font color="Maroon" title="c6">A</font>
 <span class="kw">and </span><br/><a NAME="E6:21"/><span class="lab"><font color="Green" title="E24">A6</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a2</font>
 <span class="kw">and </span><br/><a NAME="E7:21"/><span class="lab"><font color="Green" title="E25">A7</font></span>: 
<font color="Maroon" title="c4">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</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">a1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font> <a href="projpl_1.html#R5" title="PROJPL_1:pred.5">is_a_quadrangle</a> </span><br/>

<a NAME="E8:21"/>
<font color="Maroon" title="c4">b1</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Maroon" title="c6">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:21"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="ref" href="projpl_1.html#D1" target="_self" title="PROJPL_1:def.1">Def1</a></span>;<br/>
<a NAME="E9:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A8</font></span>: 
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">b1</font> <a href="projpl_1.html#NR6" title="PROJPL_1:NR.6">is_a_triangle</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E6:21"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="ref" href="projpl_1.html#T10" target="_self" title="PROJPL_1:th.10">Th10</a></span>;<br/>
<a NAME="E10:21"/>
<font color="Maroon" title="c5">b2</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Maroon" title="c6">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:21"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="ref" href="projpl_1.html#D1" target="_self" title="PROJPL_1:def.1">Def1</a></span>;<br/>
<a NAME="E11:21"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</font> <a href="projpl_1.html#NR6" title="PROJPL_1:NR.6">is_a_triangle</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E6:21"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="ref" href="projpl_1.html#T10" target="_self" title="PROJPL_1:th.10">Th10</a></span>;<br/>
<a NAME="E12:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A9</font></span>: 
<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="projpl_1.html#NR6" title="PROJPL_1:NR.6">is_a_triangle</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="projpl_1.html#T11" target="_self" title="PROJPL_1:th.11">Th11</a></span>;<br/>
<a NAME="E13:21"/>
<font color="Maroon" title="c3">a2</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Maroon" title="c7">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:21"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="projpl_1.html#D1" target="_self" title="PROJPL_1:def.1">Def1</a></span>;<br/>
<a NAME="E14:21"/><span class="kw">then </span>
<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c3">a2</font> <a href="projpl_1.html#NR6" title="PROJPL_1:NR.6">is_a_triangle</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E3:21"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E7:21"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="ref" href="projpl_1.html#T10" target="_self" title="PROJPL_1:th.10">Th10</a></span>;<br/>
<a NAME="E15:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A10</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font> <a href="projpl_1.html#NR6" title="PROJPL_1:NR.6">is_a_triangle</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="projpl_1.html#T11" target="_self" title="PROJPL_1:th.11">Th11</a></span>;<br/>
<a NAME="E16:21"/>
<font color="Maroon" title="c2">a1</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Maroon" title="c7">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:21"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="projpl_1.html#D1" target="_self" title="PROJPL_1:def.1">Def1</a></span>;<br/>
<a NAME="E17:21"/><span class="kw">then </span>
<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c2">a1</font> <a href="projpl_1.html#NR6" title="PROJPL_1:NR.6">is_a_triangle</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E3:21"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E7:21"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="ref" href="projpl_1.html#T10" target="_self" title="PROJPL_1:th.10">Th10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:21"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font> <a href="projpl_1.html#R5" title="PROJPL_1:pred.5">is_a_quadrangle</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:21"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E15:21"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="txt" href="#E12:21"><span class="lab"><font color="Green" title="E27">A9</font></span></a>, <a class="ref" href="projpl_1.html#D6" target="_self" title="PROJPL_1:def.6">Def6</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/>


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