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<b>let </b><font color="Maroon" title="c3">OTS</font> be   <a href="geomtrap.html#NM2" title="GEOMTRAP:NM.2">OrdTrapSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a'</font>, <font color="Olive" title="b2">b'</font>, <font color="Olive" title="b3">c'</font>, <font color="Olive" title="b4">d'</font>, <font color="Olive" title="b5">d1'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c3">OTS</font></span>)</span>  st <font color="Olive" title="b1">a'</font>,<font color="Olive" title="b2">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c'</font>,<font color="Olive" title="b4">d'</font> &amp; <font color="Olive" title="b1">a'</font>,<font color="Olive" title="b2">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c'</font>,<font color="Olive" title="b5">d1'</font> &amp; not <font color="Olive" title="b1">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b'</font> holds <br/><font color="Olive" title="b4">d'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">d1'</font></span><br/><b>let </b><font color="Maroon" title="c4">a'</font>, <font color="Maroon" title="c5">b'</font>, <font color="Maroon" title="c6">c'</font>, <font color="Maroon" title="c7">d'</font>, <font color="Maroon" title="c8">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="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c3">OTS</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c7">d'</font> &amp; <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c8">d1'</font> &amp; not <font color="Maroon" title="c4">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b'</font> implies <font color="Maroon" title="c7">d'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d1'</font> )</span><br/>











<b>assume </b><a NAME="E1:107"/><i><font color="Green" title="E90">A1</font></i>: 
( <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c7">d'</font> &amp; <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c8">d1'</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">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b'</font> or <font color="Maroon" title="c7">d'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d1'</font> )</span><br/>

<b>assume </b><a NAME="E2:107"/><i><font color="Green" title="E91">A2</font></i>: 
<font color="Maroon" title="c4">a'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">d'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d1'</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c9">a</font> = <font color="Maroon" title="c4">a'</font>, <font color="Maroon" title="c10">b</font> = <font color="Maroon" title="c5">b'</font>, <font color="Maroon" title="c11">c</font> = <font color="Maroon" title="c6">c'</font>, <font color="Maroon" title="c12">d</font> = <font color="Maroon" title="c7">d'</font>, <font color="Maroon" title="c13">d1</font> = <font color="Maroon" title="c8">d1'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">OTS</font> <b>by </b><i><a class="ref" href="geomtrap.html#T50" target="_self" title="GEOMTRAP:th.50">Th50</a></i>;<br/>
<a NAME="E4:107"/>
( ( <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> &amp; <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="c13">d1</font> ) or ( <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> &amp; <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="c13">d1</font>,<font color="Maroon" title="c11">c</font> ) or ( <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="c12">d</font>,<font color="Maroon" title="c11">c</font> &amp; <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="c13">d1</font> ) or ( <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="c12">d</font>,<font color="Maroon" title="c11">c</font> &amp; <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="c13">d1</font>,<font color="Maroon" title="c11">c</font> ) )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E1:107"><i><font color="Green" title="E90">A1</font></i></a>, <a class="ref" href="geomtrap.html#T51" target="_self" title="GEOMTRAP:th.51">Th51</a></i>;<br/>
<a NAME="E5:107"/><b>then </b>
( <font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d1</font> or <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c11">c</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> or <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c11">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c13">d1</font> or ( <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c9">a</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> &amp; <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c9">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c13">d1</font> ) )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E2:107"><i><font color="Green" title="E91">A2</font></i></a>, <a class="ref" href="geomtrap.html#D14" target="_self" title="GEOMTRAP:def.14">Def14</a></i>;<br/>
<a NAME="E6:107"/><b>then </b>
( <font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d1</font> or ( <font color="Maroon" title="c11">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">d</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d1</font> ) )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E2:107"><i><font color="Green" title="E91">A2</font></i></a>, <a class="ref" href="geomtrap.html#D14" target="_self" title="GEOMTRAP:def.14">Def14</a></i>;<br/>
<b>hence </b><a NAME="E7:107"/>
<font color="Maroon" title="c7">d'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d1'</font>
 ; <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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