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

<b>let </b><font color="Maroon">AS</font> be   <a href="diraf.html#NM1">AffinSpace</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">K</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">P</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">Q</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font>;<br/>









<b>assume </b><a NAME="E1:24"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">K</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">P</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="aff_4.html#K1" target="_self">Plane</a> <font color="Maroon">K</font>,<font color="Maroon">P</font> &amp; <font color="Maroon">K</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Q</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:24_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q</font>
 ;<br/><b>consider </b><font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font><b> such that </b><br/><a NAME="E3:24_1"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">K</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> )
 <b>by </b><i>, </i>;<br/><a NAME="E4:24_1"/><i><font color="Green">E37</font></i>: 
 <a href="aff_4.html#K1" target="_self">Plane</a> <font color="Maroon">K</font>,<font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="aff_4.html#K1" target="_self">Plane</a> <font color="Maroon">Q</font>,<font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/><a NAME="E5:24_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">Q</font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 <b>by </b><i>, <a class="ref" href="aff_1.html#T50">AFF_1:50</a></i>;<br/><a NAME="E6:24_1"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Q</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T57">AFF_1:57</a></i>;<br/><a NAME="E7:24_1"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T37">AFF_1:37</a></i>;<br/><b>reconsider </b><font color="Maroon">c</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> <b>by </b><i/>;<br/><a NAME="E9:24_1"/>
<font color="Maroon">c</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Q</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T37">AFF_1:37</a></i>;<br/><b>hence </b><a NAME="E10:24_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="aff_4.html#K1" target="_self">Plane</a> <font color="Maroon">K</font>,<font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:24"/>
<font color="Maroon">Q</font> <a href="tarski.html#R1">c=</a>  <a href="aff_4.html#K1" target="_self">Plane</a> <font color="Maroon">K</font>,<font color="Maroon">P</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


</div>
