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<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>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</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="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:39"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="aff_4.html#NR1" target="_self">is_plane</a> 
 <b>and </b><br/><a NAME="E2:39"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>and </b><br/><a NAME="E3:39"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E4:39"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="aff_4.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/>
<a NAME="E5:39"/><i><font color="Green">E38</font></i>: 
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 
<b>by </b><i><a class="txt" href="aff_4.html#E4:39"><i><font color="Green">E37</font></i></a>, <a class="ref" href="aff_1.html#D3">AFF_1:def 3</a></i>;<br/>
<a NAME="E6:39"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="aff_4.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>4</sub></font> <a href="aff_4.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="aff_4.html#D3" target="_self">Def3</a>, <a class="ref" href="aff_1.html#T26">AFF_1:26</a></i>;<br/>
<a NAME="E7:39"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="aff_4.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="aff_4.html#E3:39"><i><font color="Green">E36</font></i></a>, <a class="txt" href="aff_4.html#E4:39"><i><font color="Green">E37</font></i></a>, <a class="ref" href="aff_4.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E8:39"/>
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="aff_4.html#E1:39"><i><font color="Green">E34</font></i></a>, <a class="txt" href="aff_4.html#E2:39"><i><font color="Green">E35</font></i></a>, <a class="txt" href="aff_4.html#E4:39"><i><font color="Green">E37</font></i></a>, <a class="ref" href="aff_4.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E9:39"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="aff_4.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="aff_4.html#E1:39"><i><font color="Green">E34</font></i></a>, <a class="txt" href="aff_4.html#E2:39"><i><font color="Green">E35</font></i></a>, <a class="txt" href="aff_4.html#E5:39"><i><font color="Green">E38</font></i></a>, <a class="ref" href="aff_4.html#T28" target="_self">Th28</a></i>;<br/>
<b>hence </b><a NAME="E10:39"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="aff_4.html#E7:39"><i><font color="Green">E39</font></i></a></i>;<br/>


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