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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font>  st not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  holds <br/> <a href="semi_af1.html#R4" title="SEMI_AF1:pred.4">trap</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b1">o</font>,<font color="Olive" title="b1">o</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  implies  <a href="semi_af1.html#R4" title="SEMI_AF1:pred.4">trap</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c2">o</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:126"/><span class="lab"><font color="Green" title="E77">A1</font></span>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="semi_af1.html#R4" title="SEMI_AF1:pred.4">trap</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c2">o</font></span><br/>

<a NAME="E2:126"/><span class="lab"><font color="Green" title="E78">A2</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="semi_af1.html#D1" target="_self" title="SEMI_AF1:def.1">Def1</a></span>;<br/>
<a NAME="E3:126"/>
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">o</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="semi_af1.html#T40" target="_self" title="SEMI_AF1:th.40">Th40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:126"/>
 <a href="semi_af1.html#R4" title="SEMI_AF1:pred.4">trap</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c2">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126"><span class="lab"><font color="Green" title="E77">A1</font></span></a>, <a class="txt" href="#E2:126"><span class="lab"><font color="Green" title="E78">A2</font></span></a>, <a class="ref" href="semi_af1.html#D8" target="_self" title="SEMI_AF1:def.8">Def8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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