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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">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r1</font>, <font color="Olive" title="b4">r2</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">p</font>,<font color="Olive" title="b2">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b3">r1</font> &amp; <font color="Olive" title="b1">p</font>,<font color="Olive" title="b3">r1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b4">r2</font> &amp; <font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">r1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">q</font>,<font color="Olive" title="b4">r2</font> holds <br/><font color="Olive" title="b3">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">r2</font></span><br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">r1</font>, <font color="Maroon" title="c5">r2</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">p</font>,<font color="Maroon" title="c3">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">r1</font> &amp; <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">r1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">r2</font> &amp; <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">r1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">r2</font> implies <font color="Maroon" title="c4">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">r2</font> )</span><br/>









<b>assume </b><a NAME="E1:19"/>
( not <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">r1</font> &amp; <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">r1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">r2</font> &amp; <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">r1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">r2</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">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">r2</font></span><br/>

<a NAME="E2:19"/><b>then </b>
( not <font color="Maroon" title="c4">r1</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">r1</font>,<font color="Maroon" title="c3">q</font> &amp; <font color="Maroon" title="c4">r1</font>,<font color="Maroon" title="c5">r2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">r1</font>,<font color="Maroon" title="c2">p</font> &amp; <font color="Maroon" title="c4">r1</font>,<font color="Maroon" title="c5">r2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">r1</font>,<font color="Maroon" title="c3">q</font> )
 
<b>by </b><i><a class="ref" href="semi_af1.html#T28" target="_self" title="SEMI_AF1:th.28">Th28</a></i>;<br/>
<b>hence </b><a NAME="E3:19"/>
<font color="Maroon" title="c4">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">r2</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/>


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