<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="diraf.html#NM1">AffinSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:75"/><i><font color="Green">E61</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="aff_4.html#NR1" target="_self">is_plane</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="aff_4.html#NR1" target="_self">is_plane</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="aff_4.html#R1" target="_self">'||'</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:75"/><i><font color="Green">E62</font></i>: 
( not <font color="Maroon">c<sub>4</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; ( <font color="Maroon">c<sub>4</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>4</sub></font> ) &amp; ( <font color="Maroon">c<sub>5</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>7</sub></font> or <font color="Maroon">c<sub>7</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>5</sub></font> ) )
 <b>by </b><i><a class="ref" href="aff_4.html#T55" target="_self">Th55</a></i>;<br/>
<a NAME="E4:75"/>
not <font color="Maroon">c<sub>6</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>7</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:75_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E2:75_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="aff_4.html#E3:75"><i><font color="Green">E62</font></i></a>, <a class="ref" href="aff_1.html#T58">AFF_1:58</a></i>;<br/>
<b>hence </b><a NAME="E3:75_1"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_4.html#E3:75"><i><font color="Green">E62</font></i></a>, <a class="ref" href="aff_1.html#T58">AFF_1:58</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:75"/>
<font color="Maroon">c<sub>3</sub></font> <a href="aff_4.html#R1" target="_self">'||'</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:75"><i><font color="Green">E61</font></i></a>, <a class="txt" href="aff_4.html#E3:75"><i><font color="Green">E62</font></i></a>, <a class="ref" href="aff_4.html#T55" target="_self">Th55</a></i>;<br/>


</div>
