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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="incsp_1.html#L2" target="_self">IncStruct</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="incsp_1.html#NM3">PLANE</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of the <a href="incsp_1.html#U1" target="_self">Points</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>thus </b><a NAME="E1:24"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>2</sub></font> implies ( <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>2</sub></font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:24_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:24_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<b>hence </b><a NAME="E3:24_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="incsp_1.html#E1:24_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="incsp_1.html#T17" target="_self">Th17</a></i>;<br/>


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

<b>assume </b><a NAME="E2:24"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="incsp_1.html#D5" target="_self">INCSP_1:def 5</a><br/>

<b>assume </b><a NAME="E3:24"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E4:24"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:24"/>
<font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E2:24"><i><font color="Green">E19</font></i></a>, <a class="ref" href="incsp_1.html#D5" target="_self">Def5</a></i>;<br/>


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