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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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">G</font> is   <a href="incproj.html#NM2" title="INCPROJ:NM.2">IncProjSp</a> implies  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font> st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="projpl_1.html#R5" title="PROJPL_1:pred.5">is_a_quadrangle</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:22"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
<font color="Maroon" title="c1">G</font> is   <a href="incproj.html#NM2" title="INCPROJ:NM.2">IncProjSp</a>
 ; <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">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font> st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="projpl_1.html#R5" title="PROJPL_1:pred.5">is_a_quadrangle</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><br/><a NAME="E3:22"/><span class="lab"><font color="Green" title="E21">A2</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="projpl_1.html#T7" target="_self" title="PROJPL_1:th.7">Th7</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><br/><a NAME="E5:22"/><span class="lab"><font color="Green" title="E22">A3</font></span>: 
( <font color="Maroon" title="c4">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c4">a</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Maroon" title="c3">B</font> )
 <span class="kw">and </span><br/><a NAME="E6:22"/><span class="lab"><font color="Green" title="E23">A4</font></span>: 
( <font color="Maroon" title="c5">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">B</font> &amp; <font color="Maroon" title="c5">b</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Maroon" title="c2">A</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="projred1.html#T3" title="PROJRED1:th.3">PROJRED1:3</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">q</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><br/><a NAME="E8:22"/><span class="lab"><font color="Green" title="E24">A5</font></span>: 
( <font color="Maroon" title="c6">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">B</font> &amp; <font color="Maroon" title="c6">q</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Maroon" title="c2">A</font> )
 <span class="kw">and </span><br/><a NAME="E9:22"/><span class="lab"><font color="Green" title="E25">A6</font></span>: 
<font color="Maroon" title="c5">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E5:22"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="ref" href="projpl_1.html#T9" target="_self" title="PROJPL_1:th.9">Th9</a></span>;<br/>
<a NAME="E10:22"/><span class="lab"><font color="Green" title="E26">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="c5">b</font>,<font color="Maroon" title="c6">q</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">B</font> &amp; <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">q</font> <a href="projpl_1.html#R1" title="PROJPL_1:pred.1">|'</a> <font color="Maroon" title="c2">A</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:22"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="txt" href="#E8:22"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="ref" href="projpl_1.html#D1" target="_self" title="PROJPL_1:def.1">Def1</a>, <a class="ref" href="incsp_1.html#T11" title="INCSP_1:th.11">INCSP_1:11</a></span>;<br/>
<a NAME="E11:22"/><span class="lab"><font color="Green" title="E27">A8</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">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="projpl_1.html#T4" target="_self" title="PROJPL_1:th.4">Th4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">p</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><br/><a NAME="E13:22"/><span class="lab"><font color="Green" title="E28">A9</font></span>: 
( <font color="Maroon" title="c7">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c7">p</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Maroon" title="c3">B</font> )
 <span class="kw">and </span><br/><a NAME="E14:22"/><span class="lab"><font color="Green" title="E29">A10</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E5:22"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="ref" href="projpl_1.html#T9" target="_self" title="PROJPL_1:th.9">Th9</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">a</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">b</font>, <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">d</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font> st <font color="Maroon" title="c4">a</font>,<font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font>,<font color="Olive" title="b3">d</font> <a href="projpl_1.html#R5" title="PROJPL_1:pred.5">is_a_quadrangle</a> </span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c7">p</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">c</font>, <font color="Olive" title="b2">d</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font> st <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Olive" title="b1">c</font>,<font color="Olive" title="b2">d</font> <a href="projpl_1.html#R5" title="PROJPL_1:pred.5">is_a_quadrangle</a> </span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c5">b</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">d</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font> st <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c5">b</font>,<font color="Olive" title="b1">d</font> <a href="projpl_1.html#R5" title="PROJPL_1:pred.5">is_a_quadrangle</a> </span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c6">q</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="c4">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">q</font> <a href="projpl_1.html#R5" title="PROJPL_1:pred.5">is_a_quadrangle</a> </span><br/>

<a NAME="E15:22"/>
( <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c7">p</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">A</font> &amp; <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c7">p</font> <a href="projpl_1.html#R1" title="PROJPL_1:pred.1">|'</a> <font color="Maroon" title="c3">B</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="txt" href="#E13:22"><span class="lab"><font color="Green" title="E28">A9</font></span></a>, <a class="ref" href="projpl_1.html#D1" target="_self" title="PROJPL_1:def.1">Def1</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="E16:22"/>
<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">q</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="#E14:22"><span class="lab"><font color="Green" title="E29">A10</font></span></a>, <a class="txt" href="#E9:22"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E11:22"><span class="lab"><font color="Green" title="E27">A8</font></span></a>, <a class="txt" href="#E10:22"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="ref" href="projpl_1.html#T14" target="_self" title="PROJPL_1:th.14">Th14</a></span>; <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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