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<b>consider </b><font color="Maroon" title="c3">MOTS</font> being   <a href="geomtrap.html#NM1" title="GEOMTRAP:NM.1">MidOrdTrapSpace</a>;<br/>
<b>set </b><font color="Maroon" title="c4">X</font> =  <a href="geomtrap.html#K8" title="GEOMTRAP:func.8">Af</a> <font color="Maroon" title="c3">MOTS</font>;<br/>
<div><i><font color="Green" title="E93">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="114_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c7">c</font>, <font color="Maroon" title="c8">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K8" title="GEOMTRAP:func.8">Af</a> <font color="Maroon" title="c3">MOTS</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c9">a'</font>, <font color="Maroon" title="c10">b'</font>, <font color="Maroon" title="c11">c'</font>, <font color="Maroon" title="c12">d'</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">MOTS</font>;<br/><b>assume </b><a NAME="E1:114_1_1_1"/><i><font color="Green" title="E94">A2</font></i>: 
( <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">a'</font> &amp; <font color="Maroon" title="c6">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b'</font> &amp; <font color="Maroon" title="c7">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">c'</font> &amp; <font color="Maroon" title="c8">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">d'</font> )
 ;<br/><div><i><font color="Green" title="E95">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="114_1_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:114_1_1_1_1"/>
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c8">d</font>
 ;<br/><a NAME="E2:114_1_1_1_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c8">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c3">MOTS</font>
 <b>by </b><i><a class="ref" href="analoaf.html#D2" title="ANALOAF:def.2">ANALOAF:def 2</a></i>;<br/><b>hence </b><a NAME="E3:114_1_1_1_1"/>
<font color="Maroon" title="c9">a'</font>,<font color="Maroon" title="c10">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c'</font>,<font color="Maroon" title="c12">d'</font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:114_1_1_1"><i><font color="Green" title="E94">A2</font></i></a>, <a class="ref" href="analoaf.html#D2" title="ANALOAF:def.2">ANALOAF:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_1_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:114_1_1_1_2"/>
<font color="Maroon" title="c9">a'</font>,<font color="Maroon" title="c10">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c'</font>,<font color="Maroon" title="c12">d'</font>
 ;<br/><a NAME="E2:114_1_1_1_2"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c8">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c3">MOTS</font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:114_1_1_1"><i><font color="Green" title="E94">A2</font></i></a>, <a class="ref" href="analoaf.html#D2" title="ANALOAF:def.2">ANALOAF:def 2</a></i>;<br/><b>hence </b><a NAME="E3:114_1_1_1_2"/>
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c8">d</font>
 <b>by </b><i><a class="ref" href="analoaf.html#D2" title="ANALOAF:def.2">ANALOAF:def 2</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:114_1_1_1"/>
( <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c8">d</font> iff <font color="Maroon" title="c9">a'</font>,<font color="Maroon" title="c10">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c'</font>,<font color="Maroon" title="c12">d'</font> )
 <b>by </b><i><a class="txt" href="geomtrap.html#E2:114_1_1_1"><i><font color="Green" title="E95">A3</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">p</font>, <font color="Maroon" title="c6">q</font>, <font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">a1</font>, <font color="Maroon" title="c9">b</font>, <font color="Maroon" title="c10">b1</font>, <font color="Maroon" title="c11">c</font>, <font color="Maroon" title="c12">c1</font>, <font color="Maroon" title="c13">d</font>, <font color="Maroon" title="c14">d1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K8" title="GEOMTRAP:func.8">Af</a> <font color="Maroon" title="c3">MOTS</font></span>)</span>;<br/><b>assume </b><a NAME="E1:114_1_1_2"/><i><font color="Green" title="E94">A4</font></i>: 
( <font color="Maroon" title="c5">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q</font> &amp; <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">a1</font> &amp; <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c10">b1</font> &amp; <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">c1</font> &amp; <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c14">d1</font> &amp; <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c9">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c13">d</font> )
 ;<br/><b>reconsider </b><font color="Maroon" title="c15">a'</font> = <font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c16">b'</font> = <font color="Maroon" title="c9">b</font>, <font color="Maroon" title="c17">c'</font> = <font color="Maroon" title="c11">c</font>, <font color="Maroon" title="c18">d'</font> = <font color="Maroon" title="c13">d</font>, <font color="Maroon" title="c19">a1'</font> = <font color="Maroon" title="c8">a1</font>, <font color="Maroon" title="c20">b1'</font> = <font color="Maroon" title="c10">b1</font>, <font color="Maroon" title="c21">c1'</font> = <font color="Maroon" title="c12">c1</font>, <font color="Maroon" title="c22">d1'</font> = <font color="Maroon" title="c14">d1</font>, <font color="Maroon" title="c23">p'</font> = <font color="Maroon" title="c5">p</font>, <font color="Maroon" title="c24">q'</font> = <font color="Maroon" title="c6">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">MOTS</font> ;<br/><a NAME="E3:114_1_1_2"/>
( <font color="Maroon" title="c23">p'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">q'</font> &amp; <font color="Maroon" title="c23">p'</font>,<font color="Maroon" title="c24">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">a'</font>,<font color="Maroon" title="c19">a1'</font> &amp; <font color="Maroon" title="c23">p'</font>,<font color="Maroon" title="c24">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b'</font>,<font color="Maroon" title="c20">b1'</font> &amp; <font color="Maroon" title="c23">p'</font>,<font color="Maroon" title="c24">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c21">c1'</font> &amp; <font color="Maroon" title="c23">p'</font>,<font color="Maroon" title="c24">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">d'</font>,<font color="Maroon" title="c22">d1'</font> &amp; <font color="Maroon" title="c15">a'</font>,<font color="Maroon" title="c16">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c18">d'</font> )
 <b>by </b><i><a class="txt" href="geomtrap.html#E2:114_1_1"><i><font color="Green" title="E93">A1</font></i></a>, <a class="txt" href="geomtrap.html#E1:114_1_1_2"><i><font color="Green" title="E94">A4</font></i></a></i>;<br/><a NAME="E4:114_1_1_2"/><b>then </b>
<font color="Maroon" title="c19">a1'</font>,<font color="Maroon" title="c20">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">c1'</font>,<font color="Maroon" title="c22">d1'</font>
 <b>by </b><i><a class="ref" href="geomtrap.html#D13" target="_self" title="GEOMTRAP:def.13">Def13</a></i>;<br/><b>hence </b><a NAME="E5:114_1_1_2"/>
<font color="Maroon" title="c8">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">c1</font>,<font color="Maroon" title="c14">d1</font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E2:114_1_1"><i><font color="Green" title="E93">A1</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E4:114_1_1"/><b>then </b>
 <a href="geomtrap.html#K8" title="GEOMTRAP:func.8">Af</a> <font color="Maroon" title="c3">MOTS</font> is <a href="geomtrap.html#V5" title="GEOMTRAP:attr.5">Regular</a>
 
<b>by </b><i><a class="ref" href="geomtrap.html#D16" target="_self" title="GEOMTRAP:def.16">Def16</a></i>;<br/>
<b>hence </b><a NAME="E5:114_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="geomtrap.html#NM2" title="GEOMTRAP:NM.2">OrdTrapSpace</a> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="analoaf.html#V1" title="ANALOAF:attr.1">strict</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="geomtrap.html#V5" title="GEOMTRAP:attr.5">Regular</a> )
 ;<br/>


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