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<b>let </b><font color="Maroon">AS</font> be   <a href="diraf.html#NM1">AffinSpace</a>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<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">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/>









<b>assume </b><a NAME="E1:26"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> )
 ;<br/>

<a NAME="E2:26"/><b>then </b><i><font color="Green">E39</font></i>: 
(  <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> &amp;  <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font> )
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_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="E1:26_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><b>then reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> ;<br/><a NAME="E3:26_1"/>
 <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">x'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T10" target="_self">Th10</a>, </i>;<br/><a NAME="E4:26_1"/><b>then </b>
 <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">x'</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#D1" target="_self">Def1</a>, </i>;<br/><b>hence </b><a NAME="E5:26_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:26"/>
 <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="tarski.html#R1">c=</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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