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<div class="add">

<b>let </b><font color="Maroon">S</font> be    <a href="incsp_1.html#L2" target="_self">IncStruct</a> ;<br/><b>let </b><font color="Maroon">A</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">L</font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">S</font>;<br/>







<b>thus </b><a NAME="E1:14"/>
( <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">L</font> implies ( <font color="Maroon">A</font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">L</font> &amp; <font color="Maroon">B</font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">L</font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_1"/><i><font color="Green">E23</font></i>: 
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">L</font>
 ;<br/>

<a NAME="E2:14_1"/>
( <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="domain_1.html#K7">}</a></span> &amp; <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="domain_1.html#K7">}</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:14_1"/>
( <font color="Maroon">A</font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">L</font> &amp; <font color="Maroon">B</font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">L</font> )
 <b>by </b><i>, </i>;<br/>


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

<b>assume </b><a NAME="E2:14"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">A</font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">L</font> &amp; <font color="Maroon">B</font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">L</font> )
 ;<br/>

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

<b>assume </b><a NAME="E3:14"/>
<font color="Maroon">C</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="domain_1.html#K7">}</a></span>
 ;<br/>

<b>hence </b><a NAME="E4:14"/>
<font color="Maroon">C</font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">L</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>


</div>
