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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a>  iff  <a href="analoaf.html#G1" title="ANALOAF:aggr.1">AffinStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">U1</a> of <font color="Maroon" title="c1">X</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">X</font> #) is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a>  )</span><br/>

<a NAME="E1:20"/>
(  <a href="analoaf.html#G1" title="ANALOAF:aggr.1">AffinStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">U1</a> of <font color="Maroon" title="c1">X</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">X</font> #) is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a>  implies <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a>  )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="20_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:20_1"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
 <a href="analoaf.html#G1" title="ANALOAF:aggr.1">AffinStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">U1</a> of <font color="Maroon" title="c1">X</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">X</font> #) is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a> </span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="20_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">o9</font>, <font color="Olive" title="b2">a9</font>, <font color="Olive" title="b3">a19</font>, <font color="Olive" title="b4">b9</font>, <font color="Olive" title="b5">b19</font>, <font color="Olive" title="b6">c9</font>, <font color="Olive" title="b7">c19</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">a9</font> &amp; <font color="Olive" title="b1">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">a19</font> &amp; <font color="Olive" title="b1">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">b9</font> &amp; <font color="Olive" title="b1">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">b19</font> &amp; <font color="Olive" title="b1">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">c9</font> &amp; <font color="Olive" title="b1">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b7">c19</font> &amp;  not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b5">b19</font>,<font color="Olive" title="b2">a9</font> &amp;  not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b5">b19</font>,<font color="Olive" title="b6">c9</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b1">o9</font>,<font color="Olive" title="b2">a9</font>,<font color="Olive" title="b3">a19</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b1">o9</font>,<font color="Olive" title="b4">b9</font>,<font color="Olive" title="b5">b19</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b1">o9</font>,<font color="Olive" title="b6">c9</font>,<font color="Olive" title="b7">c19</font> &amp; <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">a19</font>,<font color="Olive" title="b5">b19</font> &amp; <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b4">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o9</font>,<font color="Olive" title="b6">c9</font> &amp; <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b19</font>,<font color="Olive" title="b7">c19</font> holds <br/><font color="Olive" title="b2">a9</font>,<font color="Olive" title="b6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">a19</font>,<font color="Olive" title="b7">c19</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">o9</font>, <font color="Maroon" title="c3">a9</font>, <font color="Maroon" title="c4">a19</font>, <font color="Maroon" title="c5">b9</font>, <font color="Maroon" title="c6">b19</font>, <font color="Maroon" title="c7">c9</font>, <font color="Maroon" title="c8">c19</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a9</font> &amp; <font color="Maroon" title="c2">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a19</font> &amp; <font color="Maroon" title="c2">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b9</font> &amp; <font color="Maroon" title="c2">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b19</font> &amp; <font color="Maroon" title="c2">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">c9</font> &amp; <font color="Maroon" title="c2">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c19</font> &amp;  not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">b19</font>,<font color="Maroon" title="c3">a9</font> &amp;  not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">b19</font>,<font color="Maroon" title="c7">c9</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o9</font>,<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c4">a19</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o9</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">b19</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o9</font>,<font color="Maroon" title="c7">c9</font>,<font color="Maroon" title="c8">c19</font> &amp; <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a19</font>,<font color="Maroon" title="c6">b19</font> &amp; <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o9</font>,<font color="Maroon" title="c7">c9</font> &amp; <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b19</font>,<font color="Maroon" title="c8">c19</font> implies <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c7">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a19</font>,<font color="Maroon" title="c8">c19</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:20_1_1"/>
<font color="Maroon" title="c2">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a9</font>
 <span class="kw">and </span><br/><a NAME="E2:20_1_1"/>
<font color="Maroon" title="c2">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a19</font>
 <span class="kw">and </span><br/><a NAME="E3:20_1_1"/><span class="lab"><font color="Green" title="E10">A2</font></span>: 
<font color="Maroon" title="c2">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b9</font>
 <span class="kw">and </span><br/><a NAME="E4:20_1_1"/>
<font color="Maroon" title="c2">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b19</font>
 <span class="kw">and </span><br/><a NAME="E5:20_1_1"/><span class="lab"><font color="Green" title="E11">A3</font></span>: 
<font color="Maroon" title="c2">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">c9</font>
 <span class="kw">and </span><br/><a NAME="E6:20_1_1"/>
<font color="Maroon" title="c2">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c19</font>
 <span class="kw">and </span><br/><a NAME="E7:20_1_1"/><span class="lab"><font color="Green" title="E12">A4</font></span>: 
 not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">b19</font>,<font color="Maroon" title="c3">a9</font>
 <span class="kw">and </span><br/><a NAME="E8:20_1_1"/><span class="lab"><font color="Green" title="E13">A5</font></span>: 
 not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">b19</font>,<font color="Maroon" title="c7">c9</font>
 <span class="kw">and </span><br/><a NAME="E9:20_1_1"/><span class="lab"><font color="Green" title="E14">A6</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o9</font>,<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c4">a19</font>
 <span class="kw">and </span><br/><a NAME="E10:20_1_1"/><span class="lab"><font color="Green" title="E15">A7</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o9</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">b19</font>
 <span class="kw">and </span><br/><a NAME="E11:20_1_1"/><span class="lab"><font color="Green" title="E16">A8</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o9</font>,<font color="Maroon" title="c7">c9</font>,<font color="Maroon" title="c8">c19</font>
 <span class="kw">and </span><br/><a NAME="E12:20_1_1"/><span class="lab"><font color="Green" title="E17">A9</font></span>: 
<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a19</font>,<font color="Maroon" title="c6">b19</font>
 <span class="kw">and </span><br/><a NAME="E13:20_1_1"/><span class="lab"><font color="Green" title="E18">A10</font></span>: 
<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o9</font>,<font color="Maroon" title="c7">c9</font>
 <span class="kw">and </span><br/><a NAME="E14:20_1_1"/><span class="lab"><font color="Green" title="E19">A11</font></span>: 
<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b19</font>,<font color="Maroon" title="c8">c19</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c7">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a19</font>,<font color="Maroon" title="c8">c19</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c9">o</font> = <font color="Maroon" title="c2">o9</font>, <font color="Maroon" title="c10">a</font> = <font color="Maroon" title="c3">a9</font>, <font color="Maroon" title="c11">a1</font> = <font color="Maroon" title="c4">a19</font>, <font color="Maroon" title="c12">b</font> = <font color="Maroon" title="c5">b9</font>, <font color="Maroon" title="c13">b1</font> = <font color="Maroon" title="c6">b19</font>, <font color="Maroon" title="c14">c</font> = <font color="Maroon" title="c7">c9</font>, <font color="Maroon" title="c15">c1</font> = <font color="Maroon" title="c8">c19</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="analoaf.html#G1" title="ANALOAF:aggr.1">AffinStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">U1</a> of <font color="Maroon" title="c1">X</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">X</font> #) ;<br/><a NAME="E16:20_1_1"/><span class="lab"><font color="Green" title="E20">A12</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:20_1_1"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="ref" href="analmetr.html#T40" onmouseover="rs('analmetr/T40')" onmouseout="rh()">ANALMETR:40</a></span>;<br/><a NAME="E17:20_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:20_1_1"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="analmetr.html#T40" onmouseover="rs('analmetr/T40')" onmouseout="rh()">ANALMETR:40</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c16">M</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="analoaf.html#G1" title="ANALOAF:aggr.1">AffinStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">U1</a> of <font color="Maroon" title="c1">X</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">X</font> #)<span class="kw"> such that </span><br/><a NAME="E19:20_1_1"/><span class="lab"><font color="Green" title="E21">A13</font></span>: 
<font color="Maroon" title="c16">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E20:20_1_1"/><span class="lab"><font color="Green" title="E22">A14</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">M</font>
 <span class="kw">and </span><br/><a NAME="E21:20_1_1"/><span class="lab"><font color="Green" title="E23">A15</font></span>: 
<font color="Maroon" title="c14">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">M</font>
 <span class="kw">and </span><br/><a NAME="E22:20_1_1"/><span class="lab"><font color="Green" title="E24">A16</font></span>: 
<font color="Maroon" title="c15">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">M</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T21" onmouseover="rs('aff_1/T21')" onmouseout="rh()">AFF_1:21</a></span>;<br/><a NAME="E23:20_1_1"/><span class="lab"><font color="Green" title="E25">A17</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:20_1_1"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="ref" href="analmetr.html#T40" onmouseover="rs('analmetr/T40')" onmouseout="rh()">ANALMETR:40</a></span>;<br/><a NAME="E24:20_1_1"/><span class="lab"><font color="Green" title="E26">A18</font></span>: 
 not <font color="Maroon" title="c12">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">M</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="20_1_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:20_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c9">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:20_1_1"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E2:20_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c9">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E3:20_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A19</font></span>: 
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:20_1_1_1"/>
<font color="Maroon" title="c12">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">M</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E5:20_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:20_1_1"><span class="lab"><font color="Green" title="E21">A13</font></span></a>, <a class="txt" href="#E20:20_1_1"><span class="lab"><font color="Green" title="E22">A14</font></span></a>, <a class="txt" href="#E21:20_1_1"><span class="lab"><font color="Green" title="E23">A15</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E6:20_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:20_1_1"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="txt" href="#E3:20_1_1_1"><span class="lab"><font color="Green" title="E27">A19</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:20_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:20_1_1"><span class="lab"><font color="Green" title="E25">A17</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E25:20_1_1"/>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:20_1_1"><span class="lab"><font color="Green" title="E17">A9</font></span></a>, <a class="ref" href="analmetr.html#T36" onmouseover="rs('analmetr/T36')" onmouseout="rh()">ANALMETR:36</a></span>;<br/><a NAME="E26:20_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A20</font></span>: 
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E27:20_1_1"/>
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:20_1_1"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="ref" href="analmetr.html#T40" onmouseover="rs('analmetr/T40')" onmouseout="rh()">ANALMETR:40</a></span>;<br/><a NAME="E28:20_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A21</font></span>: 
<font color="Maroon" title="c12">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" onmouseover="rs('aff_1/T7')" onmouseout="rh()">AFF_1:7</a></span>;<br/><a NAME="E29:20_1_1"/><span class="lab"><font color="Green" title="E29">A22</font></span>: 
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:20_1_1"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="ref" href="analmetr.html#T36" onmouseover="rs('analmetr/T36')" onmouseout="rh()">ANALMETR:36</a></span>;<br/><a NAME="E30:20_1_1"/><span class="lab"><font color="Green" title="E30">A23</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:20_1_1"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="ref" href="analmetr.html#T40" onmouseover="rs('analmetr/T40')" onmouseout="rh()">ANALMETR:40</a></span>;<br/><a NAME="E31:20_1_1"/>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:20_1_1"><span class="lab"><font color="Green" title="E18">A10</font></span></a>, <a class="ref" href="analmetr.html#T36" onmouseover="rs('analmetr/T36')" onmouseout="rh()">ANALMETR:36</a></span>;<br/><a NAME="E32:20_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E33:20_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c16">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:20_1_1"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="txt" href="#E19:20_1_1"><span class="lab"><font color="Green" title="E21">A13</font></span></a>, <a class="txt" href="#E20:20_1_1"><span class="lab"><font color="Green" title="E22">A14</font></span></a>, <a class="txt" href="#E21:20_1_1"><span class="lab"><font color="Green" title="E23">A15</font></span></a>, <a class="ref" href="aff_1.html#T27" onmouseover="rs('aff_1/T27')" onmouseout="rh()">AFF_1:27</a></span>;<br/><a NAME="E34:20_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E5:20_1_1"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="txt" href="#E30:20_1_1"><span class="lab"><font color="Green" title="E30">A23</font></span></a>, <a class="txt" href="#E16:20_1_1"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="txt" href="#E19:20_1_1"><span class="lab"><font color="Green" title="E21">A13</font></span></a>, <a class="txt" href="#E20:20_1_1"><span class="lab"><font color="Green" title="E22">A14</font></span></a>, <a class="txt" href="#E21:20_1_1"><span class="lab"><font color="Green" title="E23">A15</font></span></a>, <a class="txt" href="#E22:20_1_1"><span class="lab"><font color="Green" title="E24">A16</font></span></a>, <a class="txt" href="#E24:20_1_1"><span class="lab"><font color="Green" title="E26">A18</font></span></a>, <a class="txt" href="#E28:20_1_1"><span class="lab"><font color="Green" title="E28">A21</font></span></a>, <a class="txt" href="#E26:20_1_1"><span class="lab"><font color="Green" title="E27">A20</font></span></a>, <a class="txt" href="#E29:20_1_1"><span class="lab"><font color="Green" title="E29">A22</font></span></a>, <a class="ref" href="aff_2.html#D7" onmouseover="rs('aff_2/D7')" onmouseout="rh()">AFF_2:def 7</a></span>;<br/><span class="kw">hence </span><a NAME="E35:20_1_1"/>
<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c7">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a19</font>,<font color="Maroon" title="c8">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" onmouseover="rs('analmetr/T36')" onmouseout="rh()">ANALMETR:36</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:20_1"/>
<font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="conmetr.html#D5" onmouseover="rs('conmetr/D5')" onmouseout="rh()">CONMETR:def 5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:20"/>
( <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a>  iff  <a href="analoaf.html#G1" title="ANALOAF:aggr.1">AffinStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">U1</a> of <font color="Maroon" title="c1">X</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">X</font> #) is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="conmetr.html#T7" onmouseover="rs('conmetr/T7')" onmouseout="rh()">CONMETR:7</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
