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<div class="add">

<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" 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="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <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="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <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" 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="E15">A1</font></span>: 
 <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a> 
 ; <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="c1">X</font> is  <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1"><span class="kw">now </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" 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="E16">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="E17">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="E18">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="E19">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="E20">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="E21">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="E22">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="E23">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="E24">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="E25">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" 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 <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</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/><a NAME="E16:20_1_1"/><span class="lab"><font color="Green" title="E26">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="E21">A7</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">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="E22">A8</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">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 <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E19:20_1_1"/><span class="lab"><font color="Green" title="E27">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="E28">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="E29">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="E30">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" title="AFF_1:th.21">AFF_1:21</a></span>;<br/><a NAME="E23:20_1_1"/><span class="lab"><font color="Green" title="E31">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="E19">A5</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E24:20_1_1"/><span class="lab"><font color="Green" title="E32">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" 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="E26">A12</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">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" title="AFF_1:def.1">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="E33">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" title="AFF_1:th.4">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" 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="E27">A13</font></span></a>, <a class="txt" href="#E20:20_1_1"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E21:20_1_1"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">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="E16">A2</font></span></a>, <a class="txt" href="#E3:20_1_1_1"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">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="E31">A17</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</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/>


</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="E23">A9</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E26:20_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">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" title="AFF_1:th.4">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="E18">A4</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E28:20_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">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" title="AFF_1:th.7">AFF_1:7</a></span>;<br/><a NAME="E29:20_1_1"/><span class="lab"><font color="Green" title="E35">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="E25">A11</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E30:20_1_1"/><span class="lab"><font color="Green" title="E36">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="E20">A6</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">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="E24">A10</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">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" title="AFF_1:th.4">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="E17">A3</font></span></a>, <a class="txt" href="#E19:20_1_1"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E20:20_1_1"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E21:20_1_1"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="ref" href="aff_1.html#T27" title="AFF_1:th.27">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="E15">A1</font></span></a>, <a class="txt" href="#E5:20_1_1"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E30:20_1_1"><span class="lab"><font color="Green" title="E36">A23</font></span></a>, <a class="txt" href="#E16:20_1_1"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E19:20_1_1"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E20:20_1_1"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E21:20_1_1"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E22:20_1_1"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E24:20_1_1"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E28:20_1_1"><span class="lab"><font color="Green" title="E34">A21</font></span></a>, <a class="txt" href="#E26:20_1_1"><span class="lab"><font color="Green" title="E33">A20</font></span></a>, <a class="txt" href="#E29:20_1_1"><span class="lab"><font color="Green" title="E35">A22</font></span></a>, <a class="ref" href="aff_2.html#D7" title="AFF_2:def.7">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" title="ANALMETR:th.36">ANALMETR:36</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/></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" title="CONMETR:def.5">CONMETR:def 5</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/>


</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="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <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" title="CONMETR:th.7">CONMETR:7</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/>


</div>
