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<b>let </b><font color="Maroon" title="c4">b1</font>, <font color="Maroon" title="c5">b2</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#K1" title="SEMI_AF1:func.1">sum</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b1</font>,<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#K1" title="SEMI_AF1:func.1">sum</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c3">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">o</font> implies <font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:77_1_2"/><i><font color="Green" title="E66">A3</font></i>: 
 <a href="semi_af1.html#K1" title="SEMI_AF1:func.1">sum</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c3">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">o</font>
 <b>and </b><br/><a NAME="E2:77_1_2"/><i><font color="Green" title="E67">A4</font></i>: 
 <a href="semi_af1.html#K1" title="SEMI_AF1:func.1">sum</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c3">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">o</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">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font></span><br/>

<a NAME="E3:77_1_2"/>
(  <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>,<font color="Maroon" title="c4">b1</font>,<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>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c3">o</font> )
 
<b>by </b><i><a class="txt" href="#E1:77_1_2"><i><font color="Green" title="E66">A3</font></i></a>, <a class="txt" href="#E2:77_1_2"><i><font color="Green" title="E67">A4</font></i></a>, <a class="ref" href="semi_af1.html#D5" target="_self" title="SEMI_AF1:def.5">Def5</a></i>;<br/>
<a NAME="E4:77_1_2"/><b>then </b>
(  <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>,<font color="Maroon" title="c4">b1</font> &amp;  <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>,<font color="Maroon" title="c5">b2</font> )
 
<b>by </b><i><a class="ref" href="semi_af1.html#T87" target="_self" title="SEMI_AF1:th.87">Th87</a></i>;<br/>
<b>hence </b><a NAME="E5:77_1_2"/>
<font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T81" target="_self" title="SEMI_AF1:th.81">Th81</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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