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<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV0</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV0</font>, <font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV0</font>, <font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV0</font>;<br/><b>let </b><font color="Maroon">a'</font> be    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="analoaf.html#G1">AffinStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV0</font>,<font color="Maroon">P</font> #), <font color="Maroon">b'</font> be    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="analoaf.html#G1">AffinStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV0</font>,<font color="Maroon">P</font> #), <font color="Maroon">c'</font> be    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="analoaf.html#G1">AffinStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV0</font>,<font color="Maroon">P</font> #), <font color="Maroon">d'</font> be    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="analoaf.html#G1">AffinStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV0</font>,<font color="Maroon">P</font> #);<br/>



<b>assume </b><a NAME="E1:15"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a'</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b'</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c'</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d'</font> )
 ;<br/>

<div><i><font color="Green">E28</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 ;<br/><a NAME="E2:15_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="analoaf.html#U1">CONGR</a> of <a href="analoaf.html#G1">AffinStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV0</font>,<font color="Maroon">P</font> #)
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:15_1"/>
<font color="Maroon">a'</font>,<font color="Maroon">b'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c'</font>,<font color="Maroon">d'</font>
 <b>by </b><i>, <a class="ref" href="analoaf.html#D2">ANALOAF:def 2</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_2"/>
<font color="Maroon">a'</font>,<font color="Maroon">b'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c'</font>,<font color="Maroon">d'</font>
 ;<br/><a NAME="E2:15_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a'</font>,<font color="Maroon">b'</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c'</font>,<font color="Maroon">d'</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font>
 <b>by </b><i><a class="ref" href="analoaf.html#D2">ANALOAF:def 2</a></i>;<br/><b>hence </b><a NAME="E3:15_2"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:15"/>
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> iff <font color="Maroon">a'</font>,<font color="Maroon">b'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c'</font>,<font color="Maroon">d'</font> )
 <b>by </b><i/>;<br/>


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