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<b>set </b><font color="Maroon">X</font> =  <a href="geomtrap.html#K8" target="_self">Af</a> <font color="Maroon">MOS</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="115_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K8" target="_self">Af</a> <font color="Maroon">MOS</font></span>)</span>, <font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K8" target="_self">Af</a> <font color="Maroon">MOS</font></span>)</span>, <font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K8" target="_self">Af</a> <font color="Maroon">MOS</font></span>)</span>, <font color="Maroon">a1</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K8" target="_self">Af</a> <font color="Maroon">MOS</font></span>)</span>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K8" target="_self">Af</a> <font color="Maroon">MOS</font></span>)</span>, <font color="Maroon">b1</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K8" target="_self">Af</a> <font color="Maroon">MOS</font></span>)</span>, <font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K8" target="_self">Af</a> <font color="Maroon">MOS</font></span>)</span>, <font color="Maroon">c1</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K8" target="_self">Af</a> <font color="Maroon">MOS</font></span>)</span>, <font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K8" target="_self">Af</a> <font color="Maroon">MOS</font></span>)</span>, <font color="Maroon">d1</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K8" target="_self">Af</a> <font color="Maroon">MOS</font></span>)</span>;<br/><b>assume </b><a NAME="E1:115_1_1_1"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> &amp; <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font> &amp; <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">b1</font> &amp; <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">c1</font> &amp; <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font> &amp; <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/><div><i><font color="Green">E46</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="115_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K8" target="_self">Af</a> <font color="Maroon">MOS</font></span>)</span>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K8" target="_self">Af</a> <font color="Maroon">MOS</font></span>)</span>, <font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K8" target="_self">Af</a> <font color="Maroon">MOS</font></span>)</span>, <font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K8" target="_self">Af</a> <font color="Maroon">MOS</font></span>)</span>;<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 <font color="Maroon">MOS</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 <font color="Maroon">MOS</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 <font color="Maroon">MOS</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 <font color="Maroon">MOS</font>;<br/><b>assume </b><a NAME="E1:115_1_1_1_1"/><i><font color="Green">E47</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">E67</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="115_1_1_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:115_1_1_1_1_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>
 ;<br/><a NAME="E2:115_1_1_1_1_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="domain_1.html#K1">]</a></span>,<span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font></span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> the <a href="analoaf.html#U1">CONGR</a> of <font color="Maroon">MOS</font>
 <b>by </b><i><a class="ref" href="analoaf.html#D2">ANALOAF:def 2</a></i>;<br/><b>hence </b><a NAME="E3:115_1_1_1_1_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="115_1_1_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:115_1_1_1_1_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="E2:115_1_1_1_1_2"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="domain_1.html#K1">]</a></span>,<span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font></span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> the <a href="analoaf.html#U1">CONGR</a> of <font color="Maroon">MOS</font>
 <b>by </b><i>, <a class="ref" href="analoaf.html#D2">ANALOAF:def 2</a></i>;<br/><b>hence </b><a NAME="E3:115_1_1_1_1_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>
 <b>by </b><i><a class="ref" href="analoaf.html#D2">ANALOAF:def 2</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:115_1_1_1_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> 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/></div><b>end;</b></div><b>reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font>, <font color="Maroon">b'</font> = <font color="Maroon">b</font>, <font color="Maroon">c'</font> = <font color="Maroon">c</font>, <font color="Maroon">d'</font> = <font color="Maroon">d</font>, <font color="Maroon">a1'</font> = <font color="Maroon">a1</font>, <font color="Maroon">b1'</font> = <font color="Maroon">b1</font>, <font color="Maroon">c1'</font> = <font color="Maroon">c1</font>, <font color="Maroon">d1'</font> = <font color="Maroon">d1</font>, <font color="Maroon">p'</font> = <font color="Maroon">p</font>, <font color="Maroon">q'</font> = <font color="Maroon">q</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MOS</font> ;<br/><a NAME="E4:115_1_1_1"/>
( <font color="Maroon">p'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q'</font> &amp; <font color="Maroon">p'</font>,<font color="Maroon">q'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a'</font>,<font color="Maroon">a1'</font> &amp; <font color="Maroon">p'</font>,<font color="Maroon">q'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b'</font>,<font color="Maroon">b1'</font> &amp; <font color="Maroon">p'</font>,<font color="Maroon">q'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c'</font>,<font color="Maroon">c1'</font> &amp; <font color="Maroon">p'</font>,<font color="Maroon">q'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d'</font>,<font color="Maroon">d1'</font> &amp; <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="geomtrap.html#T22" target="_self">Th22</a>, </i>;<br/><a NAME="E5:115_1_1_1"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">b1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c1'</font>,<font color="Maroon">d1'</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:115_1_1_1"/>
<font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c1</font>,<font color="Maroon">d1</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:115_1_1"/>
 <a href="geomtrap.html#K8" target="_self">Af</a> <font color="Maroon">MOS</font> is <a href="geomtrap.html#V5" target="_self">Regular</a>
 <b>by </b><i><a class="ref" href="geomtrap.html#T21" target="_self">Th21</a></i>;<br/>


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