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<b>let </b><font color="Maroon" title="c1">S</font> be    <a href="incsp_1.html#L1" title="INCSP_1:struct.1">IncProjStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">L</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font>, <font color="Maroon" title="c5">C</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font>;<br/>





<b>thus </b><a NAME="E1:15"/>
( <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c2">L</font> implies ( <font color="Maroon" title="c3">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c4">B</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c5">C</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">L</font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1"/><i><font color="Green" title="E10">A1</font></i>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c2">L</font>
 ;<br/>

<a NAME="E2:15_1"/>
( <font color="Maroon" title="c3">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> &amp; <font color="Maroon" title="c4">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> &amp; <font color="Maroon" title="c5">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> )
 
<b>by </b><i><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1"/>
( <font color="Maroon" title="c3">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c4">B</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c5">C</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">L</font> )
 <b>by </b><i><a class="txt" href="incsp_1.html#E1:15_1"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="incsp_1.html#D4" target="_self" title="INCSP_1:def.4">Def4</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:15"/><i><font color="Green" title="E10">A2</font></i>: 
( <font color="Maroon" title="c3">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c4">B</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c5">C</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">L</font> )
 ;<br/>

<b>let </b><font color="Maroon" title="c6">D</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="incsp_1.html#D4" target="_self" title="INCSP_1:def.4">INCSP_1:def 4</a><br/>

<b>assume </b><a NAME="E3:15"/>
<font color="Maroon" title="c6">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span>
 ;<br/>

<b>hence </b><a NAME="E4:15"/>
<font color="Maroon" title="c6">D</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">L</font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E2:15"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/>


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