<?xml version="1.0"?>
<div class="add">

<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">a</font>, <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">q</font>, <font color="Olive" title="b5">o</font>, <font color="Olive" title="b6">c</font>, <font color="Olive" title="b7">r</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font>  st  <a href="semi_af1.html#R4" title="SEMI_AF1:pred.4">trap</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">q</font>,<font color="Olive" title="b5">o</font> &amp;  <a href="semi_af1.html#R4" title="SEMI_AF1:pred.4">trap</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">p</font>,<font color="Olive" title="b6">c</font>,<font color="Olive" title="b7">r</font>,<font color="Olive" title="b5">o</font> holds <br/><font color="Olive" title="b3">b</font>,<font color="Olive" title="b6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">q</font>,<font color="Olive" title="b7">r</font></span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">q</font>, <font color="Maroon" title="c6">o</font>, <font color="Maroon" title="c7">c</font>, <font color="Maroon" title="c8">r</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"> (  <a href="semi_af1.html#R4" title="SEMI_AF1:pred.4">trap</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">o</font> &amp;  <a href="semi_af1.html#R4" title="SEMI_AF1:pred.4">trap</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c6">o</font> implies <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c8">r</font> )</span><br/>















<b>assume </b><a NAME="E1:103"/>
(  <a href="semi_af1.html#R4" title="SEMI_AF1:pred.4">trap</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">o</font> &amp;  <a href="semi_af1.html#R4" title="SEMI_AF1:pred.4">trap</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c6">o</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c8">r</font></span><br/>

<a NAME="E2:103"/><b>then </b>
( not <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">q</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">q</font> &amp; not <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c7">c</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c8">r</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c8">r</font> )
 
<b>by </b><i><a class="ref" href="semi_af1.html#D8" target="_self" title="SEMI_AF1:def.8">Def8</a></i>;<br/>
<a NAME="E3:103"/><b>then </b>
( not <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c3">p</font> &amp; <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c5">q</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">q</font> &amp; not <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c8">r</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c8">r</font> )
 
<b>by </b><i><a class="ref" href="semi_af1.html#D2" target="_self" title="SEMI_AF1:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E4:103"/>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c8">r</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#D1" target="_self" title="SEMI_AF1:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
