<?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">o</font>, <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">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">p</font>,<font color="Olive" title="b3">c</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">p</font>,<font color="Olive" title="b4">b</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="Olive" title="b1">o</font>,<font color="Olive" title="b2">p</font> holds <br/> ex <font color="Olive" title="b5">d</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="b2">p</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b5">d</font>,<font color="Olive" title="b1">o</font></span><br/><b>let </b><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">c</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>,<font color="Maroon" title="c5">b</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="c3">p</font> implies  ex <font color="Olive" title="b1">d</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="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">d</font>,<font color="Maroon" title="c2">o</font> )</span><br/>









<b>assume </b><a NAME="E1:110"/><i><font color="Green" title="E85">A1</font></i>: 
( not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">c</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>,<font color="Maroon" title="c5">b</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="c3">p</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">d</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="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">d</font>,<font color="Maroon" title="c2">o</font></span><br/>

<b>then consider </b><font color="Maroon" title="c6">d</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="E3:110"/><i><font color="Green" title="E86">A2</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">b</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  implies ( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">d</font> ) )
 <b>by </b><i><a class="ref" href="semi_af1.html#D9" target="_self" title="SEMI_AF1:def.9">Def9</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">d</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="c3">p</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c2">o</font></span><br/>

<b>thus </b><a NAME="E4:110"/>
 <a href="semi_af1.html#R4" title="SEMI_AF1:pred.4">trap</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c2">o</font>
 <b>by </b><i><a class="txt" href="#E1:110"><i><font color="Green" title="E85">A1</font></i></a>, <a class="txt" href="#E3:110"><i><font color="Green" title="E86">A2</font></i></a>, <a class="ref" href="semi_af1.html#D8" target="_self" title="SEMI_AF1:def.8">Def8</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>
