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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">a</font>, <font color="Olive" title="b2">o</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font> holds   <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">o</font>,<font color="Olive" title="b2">o</font>, <a href="semi_af1.html#K2" title="SEMI_AF1:func.2">opposite</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">o</font></span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">o</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#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c3">o</font>, <a href="semi_af1.html#K2" title="SEMI_AF1:func.2">opposite</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">o</font></span><br/>





<a NAME="E1:85"/>
(  <a href="semi_af1.html#K1" title="SEMI_AF1:func.1">sum</a> <font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="semi_af1.html#K2" title="SEMI_AF1:func.2">opposite</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">o</font></span>)</span>,<font color="Maroon" title="c3">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">o</font> &amp;  <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c2">a</font>, <a href="semi_af1.html#K2" title="SEMI_AF1:func.2">opposite</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">o</font>, <a href="semi_af1.html#K1" title="SEMI_AF1:func.1">sum</a> <font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="semi_af1.html#K2" title="SEMI_AF1:func.2">opposite</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">o</font></span>)</span>,<font color="Maroon" title="c3">o</font> )
 
<b>by </b><i><a class="ref" href="semi_af1.html#D5" target="_self" title="SEMI_AF1:def.5">Def5</a>, <a class="ref" href="semi_af1.html#D6" target="_self" title="SEMI_AF1:def.6">Def6</a></i>;<br/>
<b>hence </b><a NAME="E2:85"/>
 <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c3">o</font>, <a href="semi_af1.html#K2" title="SEMI_AF1:func.2">opposite</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">o</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T89" target="_self" title="SEMI_AF1:th.89">Th89</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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