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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"> ( <font color="Maroon" title="c1">MS</font> is <a href="euclmetr.html#V5" title="EUCLMETR:attr.5">Moufangian</a> iff <font color="Maroon" title="c1">MS</font> is <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a> )</span><br/>

<b>set </b><font color="Maroon" title="c2">AS</font> =  <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font>;<br/>
<div><i><font color="Green" title="E20">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:21_1"/><i><font color="Green" title="E21">A2</font></i>: 
<font color="Maroon" title="c1">MS</font> is <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">MS</font> is <a href="euclmetr.html#V5" title="EUCLMETR:attr.5">Moufangian</a></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">K</font> be   <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">MS</font></span>)</span>; <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">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">a'</font>, <font color="Olive" title="b6">b'</font>, <font color="Olive" title="b7">c'</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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>  st <font color="Maroon" title="c3">K</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Olive" title="b4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Olive" title="b7">c'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; not <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</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="b4">c</font> &amp; <font color="Olive" title="b2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b5">a'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b6">b'</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">a'</font>,<font color="Olive" title="b6">b'</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">a'</font>,<font color="Olive" title="b7">c'</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">K</font> holds <br/><font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">b'</font>,<font color="Olive" title="b7">c'</font></span><br/><b>let </b><font color="Maroon" title="c4">o</font>, <font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c7">c</font>, <font color="Maroon" title="c8">a'</font>, <font color="Maroon" title="c9">b'</font>, <font color="Maroon" title="c10">c'</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">K</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c7">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c10">c'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; not <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c5">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c8">a'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c9">b'</font> &amp; <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c9">b'</font> &amp; <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c10">c'</font> &amp; <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">K</font> implies <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c10">c'</font> )</span><br/><b>assume </b><b>that </b><br/><a NAME="E1:21_1_1"/><i><font color="Green" title="E22">A3</font></i>: 
<font color="Maroon" title="c3">K</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>
 <b>and </b><br/><a NAME="E2:21_1_1"/><i><font color="Green" title="E23">A4</font></i>: 
( <font color="Maroon" title="c4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c7">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c10">c'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font> )
 <b>and </b><br/><a NAME="E3:21_1_1"/><i><font color="Green" title="E24">A5</font></i>: 
not <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font>
 <b>and </b><br/><a NAME="E4:21_1_1"/><i><font color="Green" title="E25">A6</font></i>: 
( <font color="Maroon" title="c4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c5">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b</font> )
 <b>and </b><br/><a NAME="E5:21_1_1"/><i><font color="Green" title="E26">A7</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c8">a'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c9">b'</font> )
 <b>and </b><br/><a NAME="E6:21_1_1"/><i><font color="Green" title="E27">A8</font></i>: 
( <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c9">b'</font> &amp; <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c10">c'</font> )
 <b>and </b><br/><a NAME="E7:21_1_1"/><i><font color="Green" title="E28">A9</font></i>: 
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">K</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">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c10">c'</font></span><br/><b>reconsider </b><font color="Maroon" title="c11">o1</font> = <font color="Maroon" title="c4">o</font>, <font color="Maroon" title="c12">a1</font> = <font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c13">b1</font> = <font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c14">c1</font> = <font color="Maroon" title="c7">c</font>, <font color="Maroon" title="c15">a1'</font> = <font color="Maroon" title="c8">a'</font>, <font color="Maroon" title="c16">b1'</font> = <font color="Maroon" title="c9">b'</font>, <font color="Maroon" title="c17">c1'</font> = <font color="Maroon" title="c10">c'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">MS</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E9:21_1_1"/><i><font color="Green" title="E29">A10</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c10">c'</font>
 <b>by </b><i><a class="txt" href="#E1:21_1_1"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="#E2:21_1_1"><i><font color="Green" title="E23">A4</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><a NAME="E10:21_1_1"/><b>then </b><i><font color="Green" title="E30">A11</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">o1</font>,<font color="Maroon" title="c12">a1</font>,<font color="Maroon" title="c15">a1'</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">o1</font>,<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c16">b1'</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">o1</font>,<font color="Maroon" title="c14">c1</font>,<font color="Maroon" title="c17">c1'</font> )
 <b>by </b><i><a class="txt" href="#E5:21_1_1"><i><font color="Green" title="E26">A7</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E11:21_1_1"/><i><font color="Green" title="E31">A12</font></i>: 
( <font color="Maroon" title="c11">o1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">c1</font> &amp; <font color="Maroon" title="c11">o1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">a1</font> &amp; <font color="Maroon" title="c11">o1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">b1</font> )
 <b>by </b><i><a class="txt" href="#E2:21_1_1"><i><font color="Green" title="E23">A4</font></i></a>, <a class="txt" href="#E3:21_1_1"><i><font color="Green" title="E24">A5</font></i></a>, <a class="txt" href="#E4:21_1_1"><i><font color="Green" title="E25">A6</font></i></a>, <a class="txt" href="#E7:21_1_1"><i><font color="Green" title="E28">A9</font></i></a>, <a class="ref" href="aff_1.html#T49" title="AFF_1:th.49">AFF_1:49</a></i>;<br/><a NAME="E12:21_1_1"/><i><font color="Green" title="E32">A13</font></i>: 
<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c12">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c15">a1'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:21_1_1_1"/>
<font color="Maroon" title="c12">a1</font>,<font color="Maroon" title="c13">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">a1'</font>,<font color="Maroon" title="c16">b1'</font>
 
<b>by </b><i><a class="txt" href="#E6:21_1_1"><i><font color="Green" title="E27">A8</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E2:21_1_1_1"/>
<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c12">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c15">a1'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E13:21_1_1"/><i><font color="Green" title="E33">A14</font></i>: 
<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c12">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o1</font>,<font color="Maroon" title="c14">c1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:21_1_1_2"/>
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="#E1:21_1_1"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="#E2:21_1_1"><i><font color="Green" title="E23">A4</font></i></a>, <a class="txt" href="#E4:21_1_1"><i><font color="Green" title="E25">A6</font></i></a>, <a class="txt" href="#E7:21_1_1"><i><font color="Green" title="E28">A9</font></i></a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></i>;<br/>
<a NAME="E2:21_1_1_2"/><b>then </b>
<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E3:21_1_1_2"/>
<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c12">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o1</font>,<font color="Maroon" title="c14">c1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E14:21_1_1"/><i><font color="Green" title="E34">A15</font></i>: 
<font color="Maroon" title="c12">a1</font>,<font color="Maroon" title="c14">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">a1'</font>,<font color="Maroon" title="c17">c1'</font>
 <b>by </b><i><a class="txt" href="#E6:21_1_1"><i><font color="Green" title="E27">A8</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E15:21_1_1"/><i><font color="Green" title="E35">A16</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:21_1_1_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">c</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="E2:21_1_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c5">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:21_1_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:21_1_1"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="#E2:21_1_1"><i><font color="Green" title="E23">A4</font></i></a>, <a class="txt" href="#E3:21_1_1"><i><font color="Green" title="E24">A5</font></i></a>, <a class="txt" href="#E4:21_1_1"><i><font color="Green" title="E25">A6</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E16:21_1_1"/><i><font color="Green" title="E36">A17</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:21_1_1_4"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</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="E2:21_1_1_4"/><b>then </b><i><font color="Green" title="E37">A18</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c4">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>set </b><font color="Maroon" title="c18">M</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font>;<br/>
<a NAME="E3:21_1_1_4"/><i><font color="Green" title="E38">A19</font></i>: 
( <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font> &amp; <font color="Maroon" title="c4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font> )
 
<b>by </b><i><a class="txt" href="#E2:21_1_1_4"><i><font color="Green" title="E37">A18</font></i></a>, <a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a>, <a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</a></i>;<br/>
<a NAME="E4:21_1_1_4"/>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c3">K</font>
 
<b>by </b><i><a class="txt" href="#E4:21_1_1"><i><font color="Green" title="E25">A6</font></i></a>, <a class="txt" href="#E7:21_1_1"><i><font color="Green" title="E28">A9</font></i></a>, <a class="ref" href="aff_1.html#D5" title="AFF_1:def.5">AFF_1:def 5</a></i>;<br/>
<a NAME="E5:21_1_1_4"/><b>then </b>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">K</font>
 
<b>by </b><i><a class="txt" href="#E2:21_1_1"><i><font color="Green" title="E23">A4</font></i></a>, <a class="txt" href="#E3:21_1_1_4"><i><font color="Green" title="E38">A19</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>;<br/>
<b>hence </b><a NAME="E6:21_1_1_4"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:21_1_1"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="#E2:21_1_1"><i><font color="Green" title="E23">A4</font></i></a>, <a class="txt" href="#E15:21_1_1"><i><font color="Green" title="E35">A16</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><div><i><font color="Green" title="E37">A20</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_5"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:21_1_1_5"/><i><font color="Green" title="E38">A21</font></i>: 
<font color="Maroon" title="c8">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">o</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">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c10">c'</font></span><br/><a NAME="E2:21_1_1_5"/><b>then </b><i><font color="Green" title="E39">A22</font></i>: 
<font color="Maroon" title="c9">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">o</font>
 <b>by </b><i><a class="txt" href="#E5:21_1_1"><i><font color="Green" title="E26">A7</font></i></a>, <a class="txt" href="#E6:21_1_1"><i><font color="Green" title="E27">A8</font></i></a>, <a class="txt" href="#E16:21_1_1"><i><font color="Green" title="E36">A17</font></i></a>, <a class="ref" href="aff_1.html#T69" title="AFF_1:th.69">AFF_1:69</a></i>;<br/><a NAME="E3:21_1_1_5"/>
<font color="Maroon" title="c10">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">o</font>
 <b>by </b><i><a class="txt" href="#E5:21_1_1"><i><font color="Green" title="E26">A7</font></i></a>, <a class="txt" href="#E6:21_1_1"><i><font color="Green" title="E27">A8</font></i></a>, <a class="txt" href="#E9:21_1_1"><i><font color="Green" title="E29">A10</font></i></a>, <a class="txt" href="#E15:21_1_1"><i><font color="Green" title="E35">A16</font></i></a>, <a class="txt" href="#E1:21_1_1_5"><i><font color="Green" title="E38">A21</font></i></a>, <a class="ref" href="aff_1.html#T69" title="AFF_1:th.69">AFF_1:69</a></i>;<br/><b>hence </b><a NAME="E4:21_1_1_5"/>
<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c10">c'</font>
 <b>by </b><i><a class="txt" href="#E2:21_1_1_5"><i><font color="Green" title="E39">A22</font></i></a>, <a class="ref" href="aff_1.html#T12" title="AFF_1:th.12">AFF_1:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_6"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:21_1_1_6"/><i><font color="Green" title="E38">A23</font></i>: 
<font color="Maroon" title="c8">a'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">o</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">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c10">c'</font></span><br/><div><i><font color="Green" title="E39">A24</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_6_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:21_1_1_6_1"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">a'</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">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c10">c'</font></span><br/><a NAME="E2:21_1_1_6_1"/><b>then </b><i><font color="Green" title="E40">A25</font></i>: 
( <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c6">b</font> &amp; <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c7">c</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c6">b</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c7">c</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/><a NAME="E3:21_1_1_6_1"/><b>then </b><i><font color="Green" title="E41">A26</font></i>: 
<font color="Maroon" title="c6">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b'</font>
 <b>by </b><i><a class="txt" href="#E5:21_1_1"><i><font color="Green" title="E26">A7</font></i></a>, <a class="txt" href="#E6:21_1_1"><i><font color="Green" title="E27">A8</font></i></a>, <a class="txt" href="#E16:21_1_1"><i><font color="Green" title="E36">A17</font></i></a>, <a class="ref" href="aff_1.html#T70" title="AFF_1:th.70">AFF_1:70</a></i>;<br/><a NAME="E4:21_1_1_6_1"/>
<font color="Maroon" title="c7">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">c'</font>
 <b>by </b><i><a class="txt" href="#E5:21_1_1"><i><font color="Green" title="E26">A7</font></i></a>, <a class="txt" href="#E6:21_1_1"><i><font color="Green" title="E27">A8</font></i></a>, <a class="txt" href="#E9:21_1_1"><i><font color="Green" title="E29">A10</font></i></a>, <a class="txt" href="#E15:21_1_1"><i><font color="Green" title="E35">A16</font></i></a>, <a class="txt" href="#E2:21_1_1_6_1"><i><font color="Green" title="E40">A25</font></i></a>, <a class="ref" href="aff_1.html#T70" title="AFF_1:th.70">AFF_1:70</a></i>;<br/><b>hence </b><a NAME="E5:21_1_1_6_1"/>
<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c10">c'</font>
 <b>by </b><i><a class="txt" href="#E3:21_1_1_6_1"><i><font color="Green" title="E41">A26</font></i></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_6_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:21_1_1_6_2"/><i><font color="Green" title="E40">A27</font></i>: 
<font color="Maroon" title="c5">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">a'</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">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c10">c'</font></span><br/><a NAME="E2:21_1_1_6_2"/><i><font color="Green" title="E41">A28</font></i>: 
( <font color="Maroon" title="c11">o1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">a1'</font> &amp; <font color="Maroon" title="c11">o1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">b1'</font> &amp; <font color="Maroon" title="c11">o1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">c1'</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_6_2_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:21_1_1_6_2_1"/>
<font color="Maroon" title="c11">o1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">a1'</font>
 <b>by </b><i><a class="txt" href="#E1:21_1_1_6"><i><font color="Green" title="E38">A23</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c11">o1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">b1'</font> &amp; <font color="Maroon" title="c11">o1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">c1'</font> )</span><br/>

<a NAME="E2:21_1_1_6_2_1"/><i><font color="Green" title="E42">A29</font></i>: 
( <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c8">a'</font> &amp; <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">c'</font>,<font color="Maroon" title="c8">a'</font> )
 
<b>by </b><i><a class="txt" href="#E6:21_1_1"><i><font color="Green" title="E27">A8</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E3:21_1_1_6_2_1"/>
( not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c5">a</font> &amp; not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c5">a</font> )
 
<b>by </b><i><a class="txt" href="#E15:21_1_1"><i><font color="Green" title="E35">A16</font></i></a>, <a class="txt" href="#E16:21_1_1"><i><font color="Green" title="E36">A17</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E4:21_1_1_6_2_1"/>
( <font color="Maroon" title="c11">o1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">b1'</font> &amp; <font color="Maroon" title="c11">o1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">c1'</font> )
 <b>by </b><i><a class="txt" href="#E5:21_1_1"><i><font color="Green" title="E26">A7</font></i></a>, <a class="txt" href="#E9:21_1_1"><i><font color="Green" title="E29">A10</font></i></a>, <a class="txt" href="#E1:21_1_1_6"><i><font color="Green" title="E38">A23</font></i></a>, <a class="txt" href="#E2:21_1_1_6_2_1"><i><font color="Green" title="E42">A29</font></i></a>, <a class="ref" href="aff_1.html#T69" title="AFF_1:th.69">AFF_1:69</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:21_1_1_6_2"/><i><font color="Green" title="E42">A30</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">a1</font>,<font color="Maroon" title="c15">a1'</font>,<font color="Maroon" title="c14">c1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_6_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:21_1_1_6_2_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">a1</font>,<font color="Maroon" title="c15">a1'</font>,<font color="Maroon" title="c14">c1</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="E2:21_1_1_6_2_2"/><b>then </b><i><font color="Green" title="E43">A31</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:21_1_1_6_2_2"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c4">o</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c5">a</font> )
 
<b>by </b><i><a class="txt" href="#E5:21_1_1"><i><font color="Green" title="E26">A7</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E4:21_1_1_6_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E15:21_1_1"><i><font color="Green" title="E35">A16</font></i></a>, <a class="txt" href="#E1:21_1_1_6_2"><i><font color="Green" title="E40">A27</font></i></a>, <a class="txt" href="#E2:21_1_1_6_2_2"><i><font color="Green" title="E43">A31</font></i></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:21_1_1_6_2"/>
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">a1</font>,<font color="Maroon" title="c15">a1'</font>,<font color="Maroon" title="c13">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_6_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:21_1_1_6_2_3"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">a1</font>,<font color="Maroon" title="c15">a1'</font>,<font color="Maroon" title="c13">b1</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="E2:21_1_1_6_2_3"/><b>then </b><i><font color="Green" title="E43">A32</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c6">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:21_1_1_6_2_3"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c4">o</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c5">a</font> )
 
<b>by </b><i><a class="txt" href="#E5:21_1_1"><i><font color="Green" title="E26">A7</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E4:21_1_1_6_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="#E16:21_1_1"><i><font color="Green" title="E36">A17</font></i></a>, <a class="txt" href="#E1:21_1_1_6_2"><i><font color="Green" title="E40">A27</font></i></a>, <a class="txt" href="#E2:21_1_1_6_2_3"><i><font color="Green" title="E43">A32</font></i></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E5:21_1_1_6_2"/><b>then </b>
<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c14">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c17">c1'</font>
 <b>by </b><i><a class="txt" href="#E1:21_1"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="#E10:21_1_1"><i><font color="Green" title="E30">A11</font></i></a>, <a class="txt" href="#E11:21_1_1"><i><font color="Green" title="E31">A12</font></i></a>, <a class="txt" href="#E12:21_1_1"><i><font color="Green" title="E32">A13</font></i></a>, <a class="txt" href="#E13:21_1_1"><i><font color="Green" title="E33">A14</font></i></a>, <a class="txt" href="#E14:21_1_1"><i><font color="Green" title="E34">A15</font></i></a>, <a class="txt" href="#E2:21_1_1_6_2"><i><font color="Green" title="E41">A28</font></i></a>, <a class="txt" href="#E3:21_1_1_6_2"><i><font color="Green" title="E42">A30</font></i></a>, <a class="ref" href="conmetr.html#D5" title="CONMETR:def.5">CONMETR:def 5</a></i>;<br/><b>hence </b><a NAME="E6:21_1_1_6_2"/>
<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c10">c'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E4:21_1_1_6"/>
<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c10">c'</font>
 <b>by </b><i><a class="txt" href="#E2:21_1_1_6"><i><font color="Green" title="E39">A24</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E19:21_1_1"/>
<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c10">c'</font>
 <b>by </b><i><a class="txt" href="#E17:21_1_1"><i><font color="Green" title="E37">A20</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><a NAME="E3:21_1"/><b>then </b>
 <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font> is <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a>
 <b>by </b><i><a class="ref" href="aff_2.html#D7" title="AFF_2:def.7">AFF_2:def 7</a></i>;<br/><b>hence </b><a NAME="E4:21_1"/>
<font color="Maroon" title="c1">MS</font> is <a href="euclmetr.html#V5" title="EUCLMETR:attr.5">Moufangian</a>
 <b>by </b><i><a class="ref" href="euclmetr.html#D5" target="_self" title="EUCLMETR:def.5">Def5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:21_2"/>
<font color="Maroon" title="c1">MS</font> is <a href="euclmetr.html#V5" title="EUCLMETR:attr.5">Moufangian</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">MS</font> is <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a></span><br/><a NAME="E2:21_2"/><b>then </b><i><font color="Green" title="E21">A33</font></i>: 
 <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font> is <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a>
 <b>by </b><i><a class="ref" href="euclmetr.html#D5" target="_self" title="EUCLMETR:def.5">Def5</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">o</font>, <font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">a1</font>, <font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c7">b1</font>, <font color="Maroon" title="c8">c</font>, <font color="Maroon" title="c9">c1</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"> ( <font color="Maroon" title="c3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a</font> &amp; <font color="Maroon" title="c3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a1</font> &amp; <font color="Maroon" title="c3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b</font> &amp; <font color="Maroon" title="c3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b1</font> &amp; <font color="Maroon" title="c3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font> &amp; <font color="Maroon" title="c3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">c1</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c4">a</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">c</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">c1</font> &amp; <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c6">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c7">b1</font> &amp; <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c6">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c8">c</font> &amp; <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">c1</font> implies <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c9">c1</font> )</span><br/><b>assume </b><b>that </b><br/><a NAME="E1:21_2_1"/><i><font color="Green" title="E22">A34</font></i>: 
( <font color="Maroon" title="c3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a</font> &amp; <font color="Maroon" title="c3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a1</font> &amp; <font color="Maroon" title="c3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b</font> &amp; <font color="Maroon" title="c3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b1</font> &amp; <font color="Maroon" title="c3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font> &amp; <font color="Maroon" title="c3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">c1</font> )
 <b>and </b><br/><a NAME="E2:21_2_1"/><i><font color="Green" title="E23">A35</font></i>: 
( not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c4">a</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">c</font> )
 <b>and </b><br/><a NAME="E3:21_2_1"/><i><font color="Green" title="E24">A36</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">c1</font> )
 <b>and </b><br/><a NAME="E4:21_2_1"/><i><font color="Green" title="E25">A37</font></i>: 
( <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c6">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c7">b1</font> &amp; <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c6">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c8">c</font> &amp; <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">c1</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>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c9">c1</font></span><br/><b>reconsider </b><font color="Maroon" title="c10">o'</font> = <font color="Maroon" title="c3">o</font>, <font color="Maroon" title="c11">a'</font> = <font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c12">a1'</font> = <font color="Maroon" title="c5">a1</font>, <font color="Maroon" title="c13">b'</font> = <font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c14">b1'</font> = <font color="Maroon" title="c7">b1</font>, <font color="Maroon" title="c15">c'</font> = <font color="Maroon" title="c8">c</font>, <font color="Maroon" title="c16">c1'</font> = <font color="Maroon" title="c9">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/><b>set </b><font color="Maroon" title="c17">K</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c10">o'</font>,<font color="Maroon" title="c15">c'</font>;<br/><a NAME="E6:21_2_1"/><i><font color="Green" title="E26">A38</font></i>: 
(  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c10">o'</font>,<font color="Maroon" title="c15">c'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c10">o'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c10">o'</font>,<font color="Maroon" title="c15">c'</font> &amp; <font color="Maroon" title="c15">c'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c10">o'</font>,<font color="Maroon" title="c15">c'</font> )
 <b>by </b><i><a class="txt" href="#E1:21_2_1"><i><font color="Green" title="E22">A34</font></i></a>, <a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a>, <a class="ref" href="aff_1.html#D3" title="AFF_1:def.3">AFF_1:def 3</a></i>;<br/><a NAME="E7:21_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">o'</font>,<font color="Maroon" title="c15">c'</font>,<font color="Maroon" title="c16">c1'</font>
 <b>by </b><i><a class="txt" href="#E3:21_2_1"><i><font color="Green" title="E24">A36</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E8:21_2_1"/><b>then </b><i><font color="Green" title="E27">A39</font></i>: 
( <font color="Maroon" title="c16">c1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c10">o'</font>,<font color="Maroon" title="c15">c'</font> &amp; <font color="Maroon" title="c10">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">c'</font> )
 <b>by </b><i><a class="txt" href="#E1:21_2_1"><i><font color="Green" title="E22">A34</font></i></a>, <a class="txt" href="#E6:21_2_1"><i><font color="Green" title="E26">A38</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E9:21_2_1"/><i><font color="Green" title="E28">A40</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">o'</font>,<font color="Maroon" title="c11">a'</font>,<font color="Maroon" title="c12">a1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">o'</font>,<font color="Maroon" title="c13">b'</font>,<font color="Maroon" title="c14">b1'</font> )
 <b>by </b><i><a class="txt" href="#E3:21_2_1"><i><font color="Green" title="E24">A36</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E10:21_2_1"/><i><font color="Green" title="E29">A41</font></i>: 
not <font color="Maroon" title="c13">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c10">o'</font>,<font color="Maroon" title="c15">c'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:21_2_1_1"/><i><font color="Green" title="E30">A42</font></i>: 
<font color="Maroon" title="c13">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c10">o'</font>,<font color="Maroon" title="c15">c'</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="E2:21_2_1_1"/><b>then </b>
<font color="Maroon" title="c14">b1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c10">o'</font>,<font color="Maroon" title="c15">c'</font>
 
<b>by </b><i><a class="txt" href="#E1:21_2_1"><i><font color="Green" title="E22">A34</font></i></a>, <a class="txt" href="#E6:21_2_1"><i><font color="Green" title="E26">A38</font></i></a>, <a class="txt" href="#E9:21_2_1"><i><font color="Green" title="E28">A40</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E3:21_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">b'</font>,<font color="Maroon" title="c14">b1'</font>,<font color="Maroon" title="c15">c'</font>
 
<b>by </b><i><a class="txt" href="#E6:21_2_1"><i><font color="Green" title="E26">A38</font></i></a>, <a class="txt" href="#E1:21_2_1_1"><i><font color="Green" title="E30">A42</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/>
<b>hence </b><a NAME="E4:21_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:21_2_1"><i><font color="Green" title="E23">A35</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E11:21_2_1"/><i><font color="Green" title="E30">A43</font></i>: 
<font color="Maroon" title="c13">b'</font>,<font color="Maroon" title="c11">a'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c10">o'</font>,<font color="Maroon" title="c15">c'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:21_2_1_2"/>
<font color="Maroon" title="c11">a'</font>,<font color="Maroon" title="c13">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">o'</font>,<font color="Maroon" title="c15">c'</font>
 
<b>by </b><i><a class="txt" href="#E4:21_2_1"><i><font color="Green" title="E25">A37</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E2:21_2_1_2"/><b>then </b>
<font color="Maroon" title="c11">a'</font>,<font color="Maroon" title="c13">b'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c10">o'</font>,<font color="Maroon" title="c15">c'</font>
 
<b>by </b><i><a class="txt" href="#E1:21_2_1"><i><font color="Green" title="E22">A34</font></i></a>, <a class="ref" href="aff_1.html#D4" title="AFF_1:def.4">AFF_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E3:21_2_1_2"/>
<font color="Maroon" title="c13">b'</font>,<font color="Maroon" title="c11">a'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c10">o'</font>,<font color="Maroon" title="c15">c'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T48" title="AFF_1:th.48">AFF_1:48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E12:21_2_1"/><i><font color="Green" title="E31">A44</font></i>: 
<font color="Maroon" title="c13">b'</font>,<font color="Maroon" title="c11">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">b1'</font>,<font color="Maroon" title="c12">a1'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:21_2_1_3"/>
<font color="Maroon" title="c11">a'</font>,<font color="Maroon" title="c13">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">b1'</font>
 
<b>by </b><i><a class="txt" href="#E4:21_2_1"><i><font color="Green" title="E25">A37</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E2:21_2_1_3"/>
<font color="Maroon" title="c13">b'</font>,<font color="Maroon" title="c11">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">b1'</font>,<font color="Maroon" title="c12">a1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E13:21_2_1"/><i><font color="Green" title="E32">A45</font></i>: 
<font color="Maroon" title="c13">b'</font>,<font color="Maroon" title="c15">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">b1'</font>,<font color="Maroon" title="c16">c1'</font>
 <b>by </b><i><a class="txt" href="#E4:21_2_1"><i><font color="Green" title="E25">A37</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E14:21_2_1"/>
<font color="Maroon" title="c13">b'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">a'</font>
 <b>by </b><i><a class="txt" href="#E2:21_2_1"><i><font color="Green" title="E23">A35</font></i></a>, <a class="ref" href="euclmetr.html#T1" target="_self" title="EUCLMETR:th.1">Th1</a></i>;<br/><a NAME="E15:21_2_1"/><b>then </b>
<font color="Maroon" title="c11">a'</font>,<font color="Maroon" title="c15">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">c1'</font>
 <b>by </b><i><a class="txt" href="#E2:21_2"><i><font color="Green" title="E21">A33</font></i></a>, <a class="txt" href="#E6:21_2_1"><i><font color="Green" title="E26">A38</font></i></a>, <a class="txt" href="#E8:21_2_1"><i><font color="Green" title="E27">A39</font></i></a>, <a class="txt" href="#E9:21_2_1"><i><font color="Green" title="E28">A40</font></i></a>, <a class="txt" href="#E10:21_2_1"><i><font color="Green" title="E29">A41</font></i></a>, <a class="txt" href="#E11:21_2_1"><i><font color="Green" title="E30">A43</font></i></a>, <a class="txt" href="#E12:21_2_1"><i><font color="Green" title="E31">A44</font></i></a>, <a class="txt" href="#E13:21_2_1"><i><font color="Green" title="E32">A45</font></i></a>, <a class="ref" href="aff_2.html#D7" title="AFF_2:def.7">AFF_2:def 7</a></i>;<br/><b>hence </b><a NAME="E16:21_2_1"/>
<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c9">c1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E4:21_2"/>
<font color="Maroon" title="c1">MS</font> is <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a>
 <b>by </b><i><a class="ref" href="conmetr.html#D5" title="CONMETR:def.5">CONMETR:def 5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:21"/>
( <font color="Maroon" title="c1">MS</font> is <a href="euclmetr.html#V5" title="EUCLMETR:attr.5">Moufangian</a> iff <font color="Maroon" title="c1">MS</font> is <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a> )
 <b>by </b><i><a class="txt" href="#E1:21"><i><font color="Green" title="E20">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
