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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r</font>, <font color="Olive" title="b4">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  <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a>  <a href="semi_af1.html#K1" title="SEMI_AF1:func.1">sum</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b3">r</font>,<font color="Olive" title="b4">o</font>, <a href="semi_af1.html#K1" title="SEMI_AF1:func.1">sum</a> <font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">r</font>,<font color="Olive" title="b4">o</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">r</font>, <font color="Maroon" title="c5">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a>  <a href="semi_af1.html#K1" title="SEMI_AF1:func.1">sum</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">r</font>,<font color="Maroon" title="c5">o</font>, <a href="semi_af1.html#K1" title="SEMI_AF1:func.1">sum</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">r</font>,<font color="Maroon" title="c5">o</font></span><br/>









<a NAME="E1:114"/>
 <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">r</font>, <a href="semi_af1.html#K1" title="SEMI_AF1:func.1">sum</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">r</font>,<font color="Maroon" title="c5">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="semi_af1.html#D5" target="_self" title="SEMI_AF1:def.5">Def5</a></span>;<br/>
<a NAME="E2:114"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A1</font></span>: 
 <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">o</font>, <a href="semi_af1.html#K1" title="SEMI_AF1:func.1">sum</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">r</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c4">r</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="semi_af1.html#T89" target="_self" title="SEMI_AF1:th.89">Th89</a></span>;<br/>
<a NAME="E3:114"/>
 <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">r</font>, <a href="semi_af1.html#K1" title="SEMI_AF1:func.1">sum</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">r</font>,<font color="Maroon" title="c5">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="semi_af1.html#D5" target="_self" title="SEMI_AF1:def.5">Def5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:114"/>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a>  <a href="semi_af1.html#K1" title="SEMI_AF1:func.1">sum</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">r</font>,<font color="Maroon" title="c5">o</font>, <a href="semi_af1.html#K1" title="SEMI_AF1:func.1">sum</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">r</font>,<font color="Maroon" title="c5">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:114"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="semi_af1.html#T76" target="_self" title="SEMI_AF1:th.76">Th76</a>, <a class="ref" href="semi_af1.html#T90" target="_self" title="SEMI_AF1:th.90">Th90</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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