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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:26"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
 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>
 <span class="kw">and </span><br/><a NAME="E2:26"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
( <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> )
 <span class="kw">and </span><br/><a NAME="E3:26"/><span class="lab"><font color="Green" title="E26">A3</font></span>: 
( <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> )
 <span class="kw">and </span><br/><a NAME="E4:26"/><span class="lab"><font color="Green" title="E27">A4</font></span>: 
( <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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">reconsider </span><font color="Maroon" title="c8">o9</font> = <font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c9">a19</font> = <font color="Maroon" title="c6">a1</font>, <font color="Maroon" title="c10">a29</font> = <font color="Maroon" title="c7">a2</font>, <font color="Maroon" title="c11">c19</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> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/>
<span class="kw">assume </span><a NAME="E6:26"/><span class="lab"><font color="Green" title="E28">A5</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E7:26"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="euclmetr.html#T1" target="_self" title="EUCLMETR:th.1">Th1</a></span>;<br/>
<a NAME="E8:26"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<a NAME="E9:26"/><span class="kw">then </span>
<font color="Maroon" title="c8">o9</font>,<font color="Maroon" title="c9">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">o9</font>,<font color="Maroon" title="c10">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E10:26"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">o9</font>,<font color="Maroon" title="c9">a19</font>,<font color="Maroon" title="c10">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E11:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A6</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a19</font>,<font color="Maroon" title="c10">a29</font>,<font color="Maroon" title="c8">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E12:26"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="euclmetr.html#T1" target="_self" title="EUCLMETR:th.1">Th1</a></span>;<br/>
<a NAME="E13:26"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<a NAME="E14:26"/><span class="kw">then </span>
<font color="Maroon" title="c11">c19</font>,<font color="Maroon" title="c9">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c19</font>,<font color="Maroon" title="c10">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E15:26"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">c19</font>,<font color="Maroon" title="c9">a19</font>,<font color="Maroon" title="c10">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E16:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A7</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a19</font>,<font color="Maroon" title="c10">a29</font>,<font color="Maroon" title="c11">c19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E17:26"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a19</font>,<font color="Maroon" title="c10">a29</font>,<font color="Maroon" title="c10">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/>
<a NAME="E18:26"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">o9</font>,<font color="Maroon" title="c11">c19</font>,<font color="Maroon" title="c10">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:26"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E11:26"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E16:26"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="ref" href="aff_1.html#T8" title="AFF_1:th.8">AFF_1:8</a></span>;<br/>
<a NAME="E19:26"/><span class="kw">then </span>
<font color="Maroon" title="c8">o9</font>,<font color="Maroon" title="c11">c19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">o9</font>,<font color="Maroon" title="c10">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E20:26"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E21:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A8</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E22:26"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a19</font>,<font color="Maroon" title="c10">a29</font>,<font color="Maroon" title="c9">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/>
<a NAME="E23:26"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">o9</font>,<font color="Maroon" title="c11">c19</font>,<font color="Maroon" title="c9">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:26"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E11:26"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E16:26"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="ref" href="aff_1.html#T8" title="AFF_1:th.8">AFF_1:8</a></span>;<br/>
<a NAME="E24:26"/><span class="kw">then </span>
<font color="Maroon" title="c8">o9</font>,<font color="Maroon" title="c11">c19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">o9</font>,<font color="Maroon" title="c9">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E25:26"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E26:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A9</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E27:26"/>
( <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> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:26"><span class="lab"><font color="Green" title="E28">A5</font></span></a></span>;<br/>
<a NAME="E28:26"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E26:26"><span class="lab"><font color="Green" title="E32">A9</font></span></a>, <a class="txt" href="#E21:26"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<span class="kw">hence </span><a NAME="E29:26"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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