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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">b</font>, <font color="Olive" title="b2">b'</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">a'</font>, <font color="Olive" title="b6">c'</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">b</font>,<font color="Olive" title="b2">b'</font>,<font color="Olive" title="b3">c</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp;  <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">a'</font>,<font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">b'</font> &amp;  <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">a'</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b6">c'</font> holds <br/> <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">b'</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b6">c'</font></span><br/><b>let </b><font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">b'</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">a'</font>, <font color="Maroon" title="c7">c'</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">b</font>,<font color="Maroon" title="c3">b'</font>,<font color="Maroon" title="c4">c</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp;  <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">b'</font> &amp;  <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">c'</font> implies  <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">b'</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">c'</font> )</span><br/>













<b>assume </b><a NAME="E1:51"/>
( not <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">b'</font>,<font color="Maroon" title="c4">c</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp;  <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">b'</font> &amp;  <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">a'</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">c'</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#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">b'</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">c'</font></span><br/>

<a NAME="E2:51"/><b>then </b>
( not <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">b'</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="c5">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a'</font> &amp; <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">b'</font> &amp; <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">c'</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b'</font>,<font color="Maroon" title="c7">c'</font> )
 
<b>by </b><i><a class="ref" href="semi_af1.html#D3" target="_self" title="SEMI_AF1:def.3">Def3</a>, <a class="ref" href="semi_af1.html#T54" target="_self" title="SEMI_AF1:th.54">Th54</a>, <a class="ref" href="semi_af1.html#T67" target="_self" title="SEMI_AF1:th.67">Th67</a></i>;<br/>
<a NAME="E3:51"/><b>then </b>
( not <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">b'</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">b</font>,<font color="Maroon" title="c3">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">c'</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b'</font>,<font color="Maroon" title="c7">c'</font> )
 
<b>by </b><i><a class="ref" href="semi_af1.html#D1" target="_self" title="SEMI_AF1:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E4:51"/>
 <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">b'</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">c'</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#D3" target="_self" title="SEMI_AF1:def.3">Def3</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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