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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>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <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>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="incsp_1.html#NM3">PLANE</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>











<b>thus </b><a NAME="E1:18"/>
( <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K9">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font> implies ( <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:18_1"/><i><font color="Green">E13</font></i>: 
<span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K9">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E2:18_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K9">}</a></span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K9">}</a></span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K9">}</a></span> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K9">}</a></span> )
 
<b>by </b><i><a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:18_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="incsp_1.html#E1:18_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="incsp_1.html#D5" target="_self">Def5</a></i>;<br/>


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

<b>assume </b><a NAME="E2:18"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/>

<b>let </b><font color="Maroon">c<sub>7</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="E3:18"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K9">}</a></span>
 ;<br/>

<b>hence </b><a NAME="E4:18"/>
<font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E2:18"><i><font color="Green">E13</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>


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