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<b>let </b><font color="Maroon" title="c1">MS</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</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">o</font>, <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">c1</font>, <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">a1</font>, <font color="Olive" title="b6">a2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">MS</font>  st not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">c</font>,<font color="Olive" title="b4">a</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">c1</font> &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">c1</font> &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">a1</font> &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b6">a2</font> &amp; <font color="Olive" title="b2">c</font>,<font color="Olive" title="b4">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b3">c1</font>,<font color="Olive" title="b5">a1</font> &amp; <font color="Olive" title="b2">c</font>,<font color="Olive" title="b4">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b3">c1</font>,<font color="Olive" title="b6">a2</font> holds <br/><font color="Olive" title="b5">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">a2</font></span><br/><b>let </b><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">c</font>, <font color="Maroon" title="c4">c1</font>, <font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">a1</font>, <font color="Maroon" title="c7">a2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">MS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">a</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">c1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font> &amp; <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">c1</font>,<font color="Maroon" title="c6">a1</font> &amp; <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">c1</font>,<font color="Maroon" title="c7">a2</font> implies <font color="Maroon" title="c6">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a2</font> )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:26"/><i><font color="Green" title="E24">A1</font></i>: 
( not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">a</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c1</font> )
 <b>and </b><br/><a NAME="E2:26"/><i><font color="Green" title="E25">A2</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">c1</font>
 <b>and </b><br/><a NAME="E3:26"/><i><font color="Green" title="E26">A3</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font> )
 <b>and </b><br/><a NAME="E4:26"/><i><font color="Green" title="E27">A4</font></i>: 
( <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">c1</font>,<font color="Maroon" title="c6">a1</font> &amp; <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">c1</font>,<font color="Maroon" title="c7">a2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a2</font></span><br/>

<b>assume </b><a NAME="E5:26"/><i><font color="Green" title="E28">A5</font></i>: 
<font color="Maroon" title="c6">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">a2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E6:26"/>
( <font color="Maroon" title="c5">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> )
 
<b>by </b><i><a class="txt" href="#E1:26"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="euclmetr.html#T1" target="_self" title="EUCLMETR:th.1">Th1</a></i>;<br/>
<a NAME="E7:26"/><b>then </b><i><font color="Green" title="E29">A6</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font> &amp; <font color="Maroon" title="c4">c1</font>,<font color="Maroon" title="c6">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c1</font>,<font color="Maroon" title="c7">a2</font> )
 
<b>by </b><i><a class="txt" href="#E3:26"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="#E4:26"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">o'</font> = <font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c9">a1'</font> = <font color="Maroon" title="c6">a1</font>, <font color="Maroon" title="c10">a2'</font> = <font color="Maroon" title="c7">a2</font>, <font color="Maroon" title="c11">c1'</font> = <font color="Maroon" title="c4">c1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E9:26"/>
( <font color="Maroon" title="c8">o'</font>,<font color="Maroon" title="c9">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">o'</font>,<font color="Maroon" title="c10">a2'</font> &amp; <font color="Maroon" title="c11">c1'</font>,<font color="Maroon" title="c9">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c1'</font>,<font color="Maroon" title="c10">a2'</font> )
 
<b>by </b><i><a class="txt" href="#E7:26"><i><font color="Green" title="E29">A6</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E10:26"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">o'</font>,<font color="Maroon" title="c9">a1'</font>,<font color="Maroon" title="c10">a2'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">c1'</font>,<font color="Maroon" title="c9">a1'</font>,<font color="Maroon" title="c10">a2'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:26"/><b>then </b><i><font color="Green" title="E30">A7</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1'</font>,<font color="Maroon" title="c10">a2'</font>,<font color="Maroon" title="c8">o'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1'</font>,<font color="Maroon" title="c10">a2'</font>,<font color="Maroon" title="c11">c1'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E12:26"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1'</font>,<font color="Maroon" title="c10">a2'</font>,<font color="Maroon" title="c9">a1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1'</font>,<font color="Maroon" title="c10">a2'</font>,<font color="Maroon" title="c10">a2'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/>
<a NAME="E13:26"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">o'</font>,<font color="Maroon" title="c11">c1'</font>,<font color="Maroon" title="c9">a1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">o'</font>,<font color="Maroon" title="c11">c1'</font>,<font color="Maroon" title="c10">a2'</font> )
 
<b>by </b><i><a class="txt" href="#E5:26"><i><font color="Green" title="E28">A5</font></i></a>, <a class="txt" href="#E11:26"><i><font color="Green" title="E30">A7</font></i></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></i>;<br/>
<a NAME="E14:26"/><b>then </b>
( <font color="Maroon" title="c8">o'</font>,<font color="Maroon" title="c11">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">o'</font>,<font color="Maroon" title="c9">a1'</font> &amp; <font color="Maroon" title="c8">o'</font>,<font color="Maroon" title="c11">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">o'</font>,<font color="Maroon" title="c10">a2'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:26"/><b>then </b>
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E16:26"/><b>then </b><i><font color="Green" title="E31">A8</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font> )
 
<b>by </b><i><a class="txt" href="#E1:26"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="#E2:26"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E17:26"/>
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a1</font> or <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">a2</font> )
 
<b>by </b><i><a class="txt" href="#E5:26"><i><font color="Green" title="E28">A5</font></i></a></i>;<br/>
<a NAME="E18:26"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a</font>
 
<b>by </b><i><a class="txt" href="#E3:26"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="#E16:26"><i><font color="Green" title="E31">A8</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<b>hence </b><a NAME="E19:26"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:26"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <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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