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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>;<br/><b>let </b><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">p</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font>;<br/>





<b>assume </b><a NAME="E1:110"/>
 <a href="semi_af1.html#R5" title="SEMI_AF1:pred.5">qtrap</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">p</font>
 ;<br/>

<a NAME="E2:110"/><b>then </b><i><font color="Green" title="E86">A1</font></i>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">p</font>
 
<b>by </b><i><a class="ref" href="semi_af1.html#T131" target="_self" title="SEMI_AF1:th.131">Th131</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font><b> such that </b><br/><a NAME="E4:110"/><i><font color="Green" title="E87">A2</font></i>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">r</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#T41" target="_self" title="SEMI_AF1:th.41">Th41</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font><b> such that </b><br/><a NAME="E6:110"/><i><font color="Green" title="E88">A3</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">r</font>,<font color="Maroon" title="c5">q</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp;  <a href="semi_af1.html#R5" title="SEMI_AF1:pred.5">qtrap</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">q</font> )
 <b>by </b><i><a class="ref" href="semi_af1.html#T129" target="_self" title="SEMI_AF1:th.129">Th129</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">q</font>
;<br/>

<a NAME="E7:110"/>
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">q</font> &amp; not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">r</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="c3">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">p</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">r</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">q</font> &amp;  <a href="semi_af1.html#R5" title="SEMI_AF1:pred.5">qtrap</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">q</font> )
 
<b>by </b><i><a class="txt" href="semi_af1.html#E4:110"><i><font color="Green" title="E87">A2</font></i></a>, <a class="txt" href="semi_af1.html#E6:110"><i><font color="Green" title="E88">A3</font></i></a>, <a class="ref" href="semi_af1.html#D2" target="_self" title="SEMI_AF1:def.2">Def2</a>, <a class="ref" href="semi_af1.html#T12" target="_self" title="SEMI_AF1:th.12">Th12</a>, <a class="ref" href="semi_af1.html#T131" target="_self" title="SEMI_AF1:th.131">Th131</a></i>;<br/>
<b>hence </b><a NAME="E8:110"/>
( not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">q</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp;  <a href="semi_af1.html#R5" title="SEMI_AF1:pred.5">qtrap</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">q</font> )
 <b>by </b><i><a class="txt" href="semi_af1.html#E2:110"><i><font color="Green" title="E86">A1</font></i></a>, <a class="ref" href="semi_af1.html#T39" target="_self" title="SEMI_AF1:th.39">Th39</a></i>;<br/>


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