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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">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/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_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="E1:21_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K1" 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="E3:21_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>, </i>;<br/><a NAME="E4:21_1"/><b>then </b>
 <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">x'</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E5:21_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K1" target="_self">Line</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:21"/>
 <a href="aff_1.html#K1" 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#K1" target="_self">Line</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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