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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:97_1_2"/><span class="lab"><font color="Green" title="E66">A2</font></span>: 
 <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>
 <span class="kw">and </span><br/><a NAME="E2:97_1_2"/><span class="lab"><font color="Green" title="E67">A3</font></span>: 
 <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E3:97_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="c5">b2</font>,<font color="Maroon" title="c3">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:97_1_2"><span class="lab"><font color="Green" title="E67">A3</font></span></a>, <a class="ref" href="semi_af1.html#D5" target="_self" title="SEMI_AF1:def.5">Def5</a></span>;<br/>
<a NAME="E4:97_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A4</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="semi_af1.html#T87" target="_self" title="SEMI_AF1:th.87">Th87</a></span>;<br/>
<a NAME="E5:97_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97_1_2"><span class="lab"><font color="Green" title="E66">A2</font></span></a>, <a class="ref" href="semi_af1.html#D5" target="_self" title="SEMI_AF1:def.5">Def5</a></span>;<br/>
<a NAME="E6:97_1_2"/><span class="kw">then </span>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="semi_af1.html#T87" target="_self" title="SEMI_AF1:th.87">Th87</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:97_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:97_1_2"><span class="lab"><font color="Green" title="E68">A4</font></span></a>, <a class="ref" href="semi_af1.html#T81" target="_self" title="SEMI_AF1:th.81">Th81</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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