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<b>consider </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">d</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E2:23_1_1"/><i><font color="Green" title="E20">A1</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="projpl_1.html#R5" title="PROJPL_1:pred.5">is_a_quadrangle</a> 
 <b>by </b><i><a class="ref" href="projpl_1.html#T15" target="_self" title="PROJPL_1:th.15">Th15</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">e</font> = <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">[:</a><span class="default">the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">G</font>,the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">G</font>,the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">G</font>,the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">G</font></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span> ;<br/>
<a NAME="E4:23_1_1"/><i><font color="Green" title="E21">A2</font></i>: 
( <font color="Maroon" title="c6">e</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c6">e</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c6">e</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c6">e</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T59" title="MCART_1:th.59">MCART_1:59</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">e</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">e</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> ,<font color="Maroon" title="c6">e</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a> ,<font color="Maroon" title="c6">e</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a> ,<font color="Maroon" title="c6">e</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a>  <a href="projpl_1.html#R5" title="PROJPL_1:pred.5">is_a_quadrangle</a> </span><br/>

<b>thus </b><a NAME="E5:23_1_1"/>
<font color="Maroon" title="c6">e</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> ,<font color="Maroon" title="c6">e</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a> ,<font color="Maroon" title="c6">e</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a> ,<font color="Maroon" title="c6">e</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a>  <a href="projpl_1.html#R5" title="PROJPL_1:pred.5">is_a_quadrangle</a> 
 <b>by </b><i><a class="txt" href="#E2:23_1_1"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="#E4:23_1_1"><i><font color="Green" title="E21">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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