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<b>let </b><font color="Maroon" title="c1">SAS</font> be   <a href="semi_af1.html#NM1" title="SEMI_AF1:NM.1">Semi_Affine_Space</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">a3</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font>  st <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">a2</font>,<font color="Olive" title="b3">a3</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  holds <br/>( <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b3">a3</font>,<font color="Olive" title="b2">a2</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">a2</font>,<font color="Olive" title="b1">a1</font>,<font color="Olive" title="b3">a3</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">a2</font>,<font color="Olive" title="b3">a3</font>,<font color="Olive" title="b1">a1</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b3">a3</font>,<font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">a2</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b3">a3</font>,<font color="Olive" title="b2">a2</font>,<font color="Olive" title="b1">a1</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  )</span><br/><b>let </b><font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c4">a3</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  implies ( <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c2">a1</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  ) )</span><br/>







<b>assume </b><a NAME="E1:22"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c2">a1</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  )</span><br/>

<a NAME="E2:22"/><b>then </b>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font>
 
<b>by </b><i><a class="ref" href="semi_af1.html#D2" target="_self" title="SEMI_AF1:def.2">Def2</a></i>;<br/>
<a NAME="E3:22"/><b>then </b>
( <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font> &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c2">a1</font> &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> )
 
<b>by </b><i><a class="ref" href="semi_af1.html#T18" target="_self" title="SEMI_AF1:th.18">Th18</a></i>;<br/>
<b>hence </b><a NAME="E4:22"/>
( <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c2">a1</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  )
 <b>by </b><i><a class="ref" href="semi_af1.html#D2" target="_self" title="SEMI_AF1:def.2">Def2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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