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<span class="kw">let </span><font color="Maroon" title="c1">AS</font> be   <a href="diraf.html#NM1" title="DIRAF:NM.1">AffinSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> holds <br/> (  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b2">y</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">x</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> )</span><br/>





<a NAME="E1:12"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" target="_self" title="AFF_1:th.2">Th11</a></span>;<br/>
<a NAME="E2:12"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T3" target="_self" title="AFF_1:th.3">Th12</a></span>;<br/>
<a NAME="E3:12"/>
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T3" target="_self" title="AFF_1:th.3">Th12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:12"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E2:12"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="aff_1.html#D1" target="_self" title="AFF_1:def.1">Def1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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