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<b>let </b><font color="Maroon" title="c1">G</font> be    <a href="incsp_1.html#L1" title="INCSP_1:struct.1">IncProjStr</a> ;<br/><b>let </b><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>;<br/><b>let </b><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>;<br/>













<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E19">A1</font></i>: 
( <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> )
 ;<br/>

<a NAME="E2:21"/><b>then </b><i><font color="Green" title="E20">A2</font></i>: 
( <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> &amp; <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> &amp; <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> &amp; <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> )
 
<b>by </b><i><a class="ref" href="projpl_1.html#D1" target="_self" title="PROJPL_1:def.1">Def1</a></i>;<br/>
<a NAME="E3:21"/><b>then </b><i><font color="Green" title="E21">A3</font></i>: 
<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> 
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:21"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="projpl_1.html#T10" target="_self" title="PROJPL_1:th.10">Th10</a></i>;<br/>
<a NAME="E4:21"/>
<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> 
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:21"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="projpl_1.html#E2:21"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="projpl_1.html#T10" target="_self" title="PROJPL_1:th.10">Th10</a></i>;<br/>
<a NAME="E5:21"/><b>then </b><i><font color="Green" title="E22">A4</font></i>: 
<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> 
 
<b>by </b><i><a class="ref" href="projpl_1.html#T11" target="_self" title="PROJPL_1:th.11">Th11</a></i>;<br/>
<a NAME="E6:21"/><i><font color="Green" title="E23">A5</font></i>: 
<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> 
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:21"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="projpl_1.html#E2:21"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="projpl_1.html#T10" target="_self" title="PROJPL_1:th.10">Th10</a></i>;<br/>
<a NAME="E7:21"/>
<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> 
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:21"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="projpl_1.html#E2:21"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="projpl_1.html#T10" target="_self" title="PROJPL_1:th.10">Th10</a></i>;<br/>
<a NAME="E8:21"/><b>then </b>
<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> 
 
<b>by </b><i><a class="ref" href="projpl_1.html#T11" target="_self" title="PROJPL_1:th.11">Th11</a></i>;<br/>
<b>hence </b><a NAME="E9:21"/>
<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> 
 <b>by </b><i><a class="txt" href="projpl_1.html#E3:21"><i><font color="Green" title="E21">A3</font></i></a>, <a class="txt" href="projpl_1.html#E5:21"><i><font color="Green" title="E22">A4</font></i></a>, <a class="txt" href="projpl_1.html#E6:21"><i><font color="Green" title="E23">A5</font></i></a>, <a class="ref" href="projpl_1.html#D6" target="_self" title="PROJPL_1:def.6">Def6</a></i>;<br/>


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