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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is <a href="conaffm.html#V1" title="CONAFFM:attr.1">satisfying_DES</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#V4" title="AFF_2:attr.4">Desarguesian</a> )</span><br/>

<a NAME="E1:23"/><i><font color="Green" title="E15">A1</font></i>: 
( <font color="Maroon" title="c1">X</font> is <a href="conaffm.html#V1" title="CONAFFM:attr.1">satisfying_DES</a> implies  <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font> is <a href="aff_2.html#V4" title="AFF_2:attr.4">Desarguesian</a> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1"/><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c1">X</font> is <a href="conaffm.html#V1" title="CONAFFM:attr.1">satisfying_DES</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font> is <a href="aff_2.html#V4" title="AFF_2:attr.4">Desarguesian</a></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">M</font>, <font color="Maroon" title="c4">N</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">X</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">a1</font>, <font color="Olive" title="b6">b1</font>, <font color="Olive" title="b7">c1</font> being  <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>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">M</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">N</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="b2">a</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b</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#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Olive" title="b5">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Olive" title="b3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">M</font> &amp; <font color="Olive" title="b6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">M</font> &amp; <font color="Olive" title="b4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">N</font> &amp; <font color="Olive" title="b7">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">N</font> &amp; <font color="Maroon" title="c2">A</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c3">M</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c4">N</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">M</font> &amp; <font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">N</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">a1</font>,<font color="Olive" title="b6">b1</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">a1</font>,<font color="Olive" title="b7">c1</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">b1</font>,<font color="Olive" title="b7">c1</font></span><br/><b>let </b><font color="Maroon" title="c5">o</font>, <font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">b</font>, <font color="Maroon" title="c8">c</font>, <font color="Maroon" title="c9">a1</font>, <font color="Maroon" title="c10">b1</font>, <font color="Maroon" title="c11">c1</font> be   <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">M</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">N</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b</font> &amp; <font color="Maroon" title="c5">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="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c9">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">M</font> &amp; <font color="Maroon" title="c10">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">M</font> &amp; <font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">N</font> &amp; <font color="Maroon" title="c11">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">N</font> &amp; <font color="Maroon" title="c2">A</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c3">M</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c4">N</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">M</font> &amp; <font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">N</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">c1</font> implies <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> )</span><br/><b>assume </b><a NAME="E1:23_1_1"/><i><font color="Green" title="E17">A3</font></i>: 
( <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">M</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">N</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b</font> &amp; <font color="Maroon" title="c5">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="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c9">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">M</font> &amp; <font color="Maroon" title="c10">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">M</font> &amp; <font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">N</font> &amp; <font color="Maroon" title="c11">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">N</font> &amp; <font color="Maroon" title="c2">A</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c3">M</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c4">N</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">M</font> &amp; <font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">N</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">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="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font></span><br/><b>assume </b><a NAME="E2:23_1_1"/><i><font color="Green" title="E18">A4</font></i>: 
not <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><b>reconsider </b><font color="Maroon" title="c12">o'</font> = <font color="Maroon" title="c5">o</font>, <font color="Maroon" title="c13">a'</font> = <font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c14">a1'</font> = <font color="Maroon" title="c9">a1</font>, <font color="Maroon" title="c15">b'</font> = <font color="Maroon" title="c7">b</font>, <font color="Maroon" title="c16">b1'</font> = <font color="Maroon" title="c10">b1</font>, <font color="Maroon" title="c17">c'</font> = <font color="Maroon" title="c8">c</font>, <font color="Maroon" title="c18">c1'</font> = <font color="Maroon" title="c11">c1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E4:23_1_1"/><i><font color="Green" title="E19">A5</font></i>: 
( <font color="Maroon" title="c2">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c3">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c3">M</font> &amp; <font color="Maroon" title="c4">N</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c4">N</font> )
 <b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E5:23_1_1"/><i><font color="Green" title="E20">A6</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c14">a1'</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c16">b1'</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c18">c1'</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:23_1_1_1"/>
( <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font> &amp; <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font> &amp; <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font> )
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E4:23_1_1"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E2:23_1_1_1"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">b1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c11">c1</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:23_1_1_1"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c14">a1'</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c16">b1'</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c18">c1'</font> )
 <b>by </b><i><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="E6:23_1_1"/><i><font color="Green" title="E21">A7</font></i>: 
( <font color="Maroon" title="c12">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">a1'</font> &amp; <font color="Maroon" title="c12">o'</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="c12">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c1'</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1_1_2"/><i><font color="Green" title="E22">A8</font></i>: 
(  not <font color="Maroon" title="c12">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">a1'</font> or  not <font color="Maroon" title="c12">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">b1'</font> or  not <font color="Maroon" title="c12">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c1'</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><i><font color="Green" title="E23">A9</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:23_1_1_2_1"/><i><font color="Green" title="E24">A10</font></i>: 
<font color="Maroon" title="c12">o'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">a1'</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="E2:23_1_1_2_1"/><i><font color="Green" title="E25">A11</font></i>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1_1_2_1_1"/><i><font color="Green" title="E26">A12</font></i>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">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="E2:23_1_1_2_1_1"/><i><font color="Green" title="E27">A13</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_2_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1_1_2_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</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="E2:23_1_1_2_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:23_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:23_1_1_2_1_1_1"/><b>then </b>
( <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">M</font> )
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:23_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c3">M</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:23_1_1_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</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="E3:23_1_1_2_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">b1</font>
 
<b>by </b><i><a class="txt" href="#E5:23_1_1"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:23_1_1_2_1_1"/><b>then </b><i><font color="Green" title="E28">A14</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E5:23_1_1_2_1_1"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c10">b1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_2_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:23_1_1_2_1_1_2"/><i><font color="Green" title="E29">A15</font></i>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E4:23_1_1"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E2:23_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E1:23_1_1_2_1"><i><font color="Green" title="E24">A10</font></i></a>, <a class="txt" href="#E1:23_1_1_2_1_1"><i><font color="Green" title="E26">A12</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:23_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E4:23_1_1_2_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:23_1_1_2_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E6:23_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E7:23_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E1:23_1_1_2_1_1_2"><i><font color="Green" title="E29">A15</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E8:23_1_1_2_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c10">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:23_1_1_2_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</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="E10:23_1_1_2_1_1_2"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c10">b1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</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="E6:23_1_1_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:23_1_1_2_1_1"><i><font color="Green" title="E26">A12</font></i></a>, <a class="txt" href="#E2:23_1_1_2_1_1"><i><font color="Green" title="E27">A13</font></i></a>, <a class="txt" href="#E4:23_1_1_2_1_1"><i><font color="Green" title="E28">A14</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</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="E3:23_1_1_2_1"/>
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">c1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1_1_2_1_2"/><i><font color="Green" title="E26">A16</font></i>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">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="E2:23_1_1_2_1_2"/><i><font color="Green" title="E27">A17</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_2_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1_1_2_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</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="E2:23_1_1_2_1_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:23_1_1_2_1_2_1"/><b>then </b>
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:23_1_1_2_1_2_1"/><b>then </b>
( <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">N</font> )
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:23_1_1_2_1_2_1"/><b>then </b>
<font color="Maroon" title="c2">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c4">N</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:23_1_1_2_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</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="E3:23_1_1_2_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c11">c1</font>
 
<b>by </b><i><a class="txt" href="#E5:23_1_1"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:23_1_1_2_1_2"/><b>then </b><i><font color="Green" title="E28">A18</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E5:23_1_1_2_1_2"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c11">c1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_2_1_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:23_1_1_2_1_2_2"/><i><font color="Green" title="E29">A19</font></i>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E4:23_1_1"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E2:23_1_1_2_1_2_2"/><b>then </b>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E1:23_1_1_2_1"><i><font color="Green" title="E24">A10</font></i></a>, <a class="txt" href="#E1:23_1_1_2_1_2"><i><font color="Green" title="E26">A16</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:23_1_1_2_1_2_2"/><b>then </b>
<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E4:23_1_1_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:23_1_1_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E6:23_1_1_2_1_2_2"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E7:23_1_1_2_1_2_2"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E1:23_1_1_2_1_2_2"><i><font color="Green" title="E29">A19</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E8:23_1_1_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c11">c1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:23_1_1_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E10:23_1_1_2_1_2_2"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c11">c1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</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="E6:23_1_1_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:23_1_1_2_1_2"><i><font color="Green" title="E26">A16</font></i></a>, <a class="txt" href="#E2:23_1_1_2_1_2"><i><font color="Green" title="E27">A17</font></i></a>, <a class="txt" href="#E4:23_1_1_2_1_2"><i><font color="Green" title="E28">A18</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</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="E4:23_1_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:23_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E2:23_1_1_2_1"><i><font color="Green" title="E25">A11</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><i><font color="Green" title="E24">A20</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:23_1_1_2_2"/><i><font color="Green" title="E25">A21</font></i>: 
<font color="Maroon" title="c12">o'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">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="E2:23_1_1_2_2"/><i><font color="Green" title="E26">A22</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1_1_2_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</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="E2:23_1_1_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:23_1_1_2_2_1"/><b>then </b>
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:23_1_1_2_2_1"/><b>then </b>
( <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">M</font> )
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:23_1_1_2_2_1"/><b>then </b>
<font color="Maroon" title="c2">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c3">M</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:23_1_1_2_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</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="E3:23_1_1_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 <b>by </b><i><a class="txt" href="#E5:23_1_1"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E4:23_1_1_2_2"/><b>then </b><i><font color="Green" title="E27">A23</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E5:23_1_1_2_2"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c9">a1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_2_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:23_1_1_2_2_2"/><i><font color="Green" title="E28">A24</font></i>: 
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E4:23_1_1"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E2:23_1_1_2_2_2"/><b>then </b>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E2:23_1_1_2"><i><font color="Green" title="E23">A9</font></i></a>, <a class="txt" href="#E1:23_1_1_2_2"><i><font color="Green" title="E25">A21</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:23_1_1_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:23_1_1_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">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/>
<a NAME="E5:23_1_1_2_2_2"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E6:23_1_1_2_2_2"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E7:23_1_1_2_2_2"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E1:23_1_1_2_2_2"><i><font color="Green" title="E28">A24</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E8:23_1_1_2_2_2"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E9:23_1_1_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c9">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:23_1_1_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</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="E11:23_1_1_2_2_2"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c9">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</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="E6:23_1_1_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:23_1_1_2"><i><font color="Green" title="E23">A9</font></i></a>, <a class="txt" href="#E2:23_1_1_2_2"><i><font color="Green" title="E26">A22</font></i></a>, <a class="txt" href="#E4:23_1_1_2_2"><i><font color="Green" title="E27">A23</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</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="23_1_1_2_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:23_1_1_2_3"/><i><font color="Green" title="E25">A25</font></i>: 
<font color="Maroon" title="c12">o'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">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="E2:23_1_1_2_3"/><i><font color="Green" title="E26">A26</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_2_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1_1_2_3_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</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="E2:23_1_1_2_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:23_1_1_2_3_1"/><b>then </b>
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:23_1_1_2_3_1"/><b>then </b>
( <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">N</font> )
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:23_1_1_2_3_1"/><b>then </b>
<font color="Maroon" title="c2">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c4">N</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:23_1_1_2_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</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="E3:23_1_1_2_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 <b>by </b><i><a class="txt" href="#E5:23_1_1"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E4:23_1_1_2_3"/><b>then </b><i><font color="Green" title="E27">A27</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E5:23_1_1_2_3"/>
<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">a1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_2_3_2"><b>proof </b></a><div class="add">

<a NAME="E1:23_1_1_2_3_2"/><i><font color="Green" title="E28">A28</font></i>: 
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E4:23_1_1"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E2:23_1_1_2_3_2"/><b>then </b>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E2:23_1_1_2"><i><font color="Green" title="E23">A9</font></i></a>, <a class="txt" href="#E1:23_1_1_2_3"><i><font color="Green" title="E25">A25</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:23_1_1_2_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:23_1_1_2_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">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/>
<a NAME="E5:23_1_1_2_3_2"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E6:23_1_1_2_3_2"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E7:23_1_1_2_3_2"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E1:23_1_1_2_3_2"><i><font color="Green" title="E28">A28</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E8:23_1_1_2_3_2"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E9:23_1_1_2_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:23_1_1_2_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</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="E11:23_1_1_2_3_2"/>
<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</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="E6:23_1_1_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:23_1_1_2"><i><font color="Green" title="E23">A9</font></i></a>, <a class="txt" href="#E2:23_1_1_2_3"><i><font color="Green" title="E26">A26</font></i></a>, <a class="txt" href="#E4:23_1_1_2_3"><i><font color="Green" title="E27">A27</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</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="E5:23_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:23_1_1_2"><i><font color="Green" title="E22">A8</font></i></a>, <a class="txt" href="#E2:23_1_1_2"><i><font color="Green" title="E23">A9</font></i></a>, <a class="txt" href="#E3:23_1_1_2"><i><font color="Green" title="E24">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="E7:23_1_1"/><i><font color="Green" title="E22">A29</font></i>: 
( not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c13">a'</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c17">c'</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1_1_3"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c13">a'</font> or  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c17">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="E2:23_1_1_3"/><b>then </b><i><font color="Green" title="E23">A30</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c6">a</font> or  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c8">c</font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:23_1_1_3"/><i><font color="Green" title="E24">A31</font></i>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">a1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1_1_3_1"/><i><font color="Green" title="E25">A32</font></i>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">a1</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="E2:23_1_1_3_1"/><i><font color="Green" title="E26">A33</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_3_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1_1_3_1_1"/><i><font color="Green" title="E27">A34</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">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="E2:23_1_1_3_1_1"/><i><font color="Green" title="E28">A35</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_3_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1_1_3_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">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="E2:23_1_1_3_1_1_1"/><b>then </b>
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E3:23_1_1_3_1_1_1"/><b>then </b><i><font color="Green" title="E29">A36</font></i>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E4:23_1_1_3_1_1_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">M</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:23_1_1_3_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c3">M</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E3:23_1_1_3_1_1_1"><i><font color="Green" title="E29">A36</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:23_1_1_3_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</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="E3:23_1_1_3_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">b1</font>
 
<b>by </b><i><a class="txt" href="#E5:23_1_1"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E4:23_1_1_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E1:23_1_1_3_1"><i><font color="Green" title="E25">A32</font></i></a>, <a class="txt" href="#E1:23_1_1_3_1_1"><i><font color="Green" title="E27">A34</font></i></a>, <a class="txt" href="#E2:23_1_1_3_1_1"><i><font color="Green" title="E28">A35</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</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="E3:23_1_1_3_1"/>
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">c1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_3_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1_1_3_1_2"/><i><font color="Green" title="E27">A37</font></i>: 
<font color="Maroon" title="c8">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">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="E2:23_1_1_3_1_2"/><i><font color="Green" title="E28">A38</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_3_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1_1_3_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">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="E2:23_1_1_3_1_2_1"/><b>then </b>
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E3:23_1_1_3_1_2_1"/><b>then </b><i><font color="Green" title="E29">A39</font></i>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E4:23_1_1_3_1_2_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">N</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:23_1_1_3_1_2_1"/><b>then </b>
<font color="Maroon" title="c2">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c4">N</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E3:23_1_1_3_1_2_1"><i><font color="Green" title="E29">A39</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:23_1_1_3_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</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="E3:23_1_1_3_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c11">c1</font>
 
<b>by </b><i><a class="txt" href="#E5:23_1_1"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E4:23_1_1_3_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E1:23_1_1_3_1"><i><font color="Green" title="E25">A32</font></i></a>, <a class="txt" href="#E1:23_1_1_3_1_2"><i><font color="Green" title="E27">A37</font></i></a>, <a class="txt" href="#E2:23_1_1_3_1_2"><i><font color="Green" title="E28">A38</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</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="E4:23_1_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:23_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E2:23_1_1_3_1"><i><font color="Green" title="E26">A33</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>
<a NAME="E4:23_1_1_3"/>
<font color="Maroon" title="c7">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1_1_3_2"/><i><font color="Green" title="E25">A40</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">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="E2:23_1_1_3_2"/><i><font color="Green" title="E26">A41</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_3_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1_1_3_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</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="E2:23_1_1_3_2_1"/><b>then </b>
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">M</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E3:23_1_1_3_2_1"/><b>then </b><i><font color="Green" title="E27">A42</font></i>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">M</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E4:23_1_1_3_2_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:23_1_1_3_2_1"/><b>then </b>
<font color="Maroon" title="c2">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c3">M</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E3:23_1_1_3_2_1"><i><font color="Green" title="E27">A42</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:23_1_1_3_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</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="E3:23_1_1_3_2"/><i><font color="Green" title="E27">A43</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 
<b>by </b><i><a class="txt" href="#E5:23_1_1"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:23_1_1_3_2"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c9">a1</font>
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E1:23_1_1_3_2"><i><font color="Green" title="E25">A40</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:23_1_1_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:23_1_1_3"><i><font color="Green" title="E24">A31</font></i></a>, <a class="txt" href="#E2:23_1_1_3_2"><i><font color="Green" title="E26">A41</font></i></a>, <a class="txt" href="#E3:23_1_1_3_2"><i><font color="Green" title="E27">A43</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</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="E5:23_1_1_3"/><b>then </b>
( <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">M</font> or <font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> )
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E2:23_1_1_3"><i><font color="Green" title="E23">A30</font></i></a>, <a class="txt" href="#E3:23_1_1_3"><i><font color="Green" title="E24">A31</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E6:23_1_1_3"/><b>then </b><i><font color="Green" title="E25">A44</font></i>: 
( <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">M</font> or <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">A</font> )
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E7:23_1_1_3"/>
( <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">N</font> )
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E8:23_1_1_3"/><b>then </b>
( <font color="Maroon" title="c2">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c3">M</font> or <font color="Maroon" title="c2">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c4">N</font> )
 
<b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E6:23_1_1_3"><i><font color="Green" title="E25">A44</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E9:23_1_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</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="E8:23_1_1"/>
( <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c16">b1'</font> &amp; <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c18">c1'</font> )
 <b>by </b><i><a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E9:23_1_1"/><b>then </b>
<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c18">c1'</font>
 <b>by </b><i><a class="txt" href="#E1:23_1"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="#E1:23_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E5:23_1_1"><i><font color="Green" title="E20">A6</font></i></a>, <a class="txt" href="#E6:23_1_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="#E7:23_1_1"><i><font color="Green" title="E22">A29</font></i></a>, <a class="ref" href="conaffm.html#D1" title="CONAFFM:def.1">CONAFFM:def 1</a></i>;<br/><b>hence </b><a NAME="E10:23_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:23_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <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="E3:23_1"/>
 <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font> is <a href="aff_2.html#V4" title="AFF_2:attr.4">Desarguesian</a>
 <b>by </b><i><a class="ref" href="aff_2.html#D4" title="AFF_2:def.4">AFF_2:def 4</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="E2:23"/>
(  <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font> is <a href="aff_2.html#V4" title="AFF_2:attr.4">Desarguesian</a> implies <font color="Maroon" title="c1">X</font> is <a href="conaffm.html#V1" title="CONAFFM:attr.1">satisfying_DES</a> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_2"/><i><font color="Green" title="E16">A45</font></i>: 
 <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font> is <a href="aff_2.html#V4" title="AFF_2:attr.4">Desarguesian</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">X</font> is <a href="conaffm.html#V1" title="CONAFFM:attr.1">satisfying_DES</a></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">o'</font>, <font color="Maroon" title="c3">a'</font>, <font color="Maroon" title="c4">a1'</font>, <font color="Maroon" title="c5">b'</font>, <font color="Maroon" title="c6">b1'</font>, <font color="Maroon" title="c7">c'</font>, <font color="Maroon" title="c8">c1'</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a'</font> &amp; <font color="Maroon" title="c2">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a1'</font> &amp; <font color="Maroon" title="c2">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b'</font> &amp; <font color="Maroon" title="c2">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1'</font> &amp; <font color="Maroon" title="c2">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">c'</font> &amp; <font color="Maroon" title="c2">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c1'</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">b1'</font>,<font color="Maroon" title="c3">a'</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a'</font>,<font color="Maroon" title="c4">a1'</font>,<font color="Maroon" title="c7">c'</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o'</font>,<font color="Maroon" title="c3">a'</font>,<font color="Maroon" title="c4">a1'</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o'</font>,<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">b1'</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o'</font>,<font color="Maroon" title="c7">c'</font>,<font color="Maroon" title="c8">c1'</font> &amp; <font color="Maroon" title="c3">a'</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1'</font>,<font color="Maroon" title="c6">b1'</font> &amp; <font color="Maroon" title="c3">a'</font>,<font color="Maroon" title="c7">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1'</font>,<font color="Maroon" title="c8">c1'</font> implies <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c7">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1'</font>,<font color="Maroon" title="c8">c1'</font> )</span><br/><b>assume </b><a NAME="E1:23_2_1"/><i><font color="Green" title="E17">A46</font></i>: 
( <font color="Maroon" title="c2">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a'</font> &amp; <font color="Maroon" title="c2">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a1'</font> &amp; <font color="Maroon" title="c2">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b'</font> &amp; <font color="Maroon" title="c2">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1'</font> &amp; <font color="Maroon" title="c2">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">c'</font> &amp; <font color="Maroon" title="c2">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c1'</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">b1'</font>,<font color="Maroon" title="c3">a'</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a'</font>,<font color="Maroon" title="c4">a1'</font>,<font color="Maroon" title="c7">c'</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o'</font>,<font color="Maroon" title="c3">a'</font>,<font color="Maroon" title="c4">a1'</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o'</font>,<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">b1'</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o'</font>,<font color="Maroon" title="c7">c'</font>,<font color="Maroon" title="c8">c1'</font> &amp; <font color="Maroon" title="c3">a'</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1'</font>,<font color="Maroon" title="c6">b1'</font> &amp; <font color="Maroon" title="c3">a'</font>,<font color="Maroon" title="c7">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1'</font>,<font color="Maroon" title="c8">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="c5">b'</font>,<font color="Maroon" title="c7">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1'</font>,<font color="Maroon" title="c8">c1'</font></span><br/><b>reconsider </b><font color="Maroon" title="c9">o</font> = <font color="Maroon" title="c2">o'</font>, <font color="Maroon" title="c10">a</font> = <font color="Maroon" title="c3">a'</font>, <font color="Maroon" title="c11">a1</font> = <font color="Maroon" title="c4">a1'</font>, <font color="Maroon" title="c12">b</font> = <font color="Maroon" title="c5">b'</font>, <font color="Maroon" title="c13">b1</font> = <font color="Maroon" title="c6">b1'</font>, <font color="Maroon" title="c14">c</font> = <font color="Maroon" title="c7">c'</font>, <font color="Maroon" title="c15">c1</font> = <font color="Maroon" title="c8">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">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E3:23_2_1"/><i><font color="Green" title="E18">A47</font></i>: 
( 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> &amp; not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c14">c</font> &amp;  <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> &amp;  <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> &amp;  <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> )
 <b>by </b><i><a class="txt" href="#E1:23_2_1"><i><font color="Green" title="E17">A46</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><b>then consider </b><font color="Maroon" title="c16">A</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><b> such that </b><br/><a NAME="E5:23_2_1"/><i><font color="Green" title="E19">A48</font></i>: 
( <font color="Maroon" title="c16">A</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c9">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">A</font> &amp; <font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">A</font> &amp; <font color="Maroon" title="c11">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">A</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><b>consider </b><font color="Maroon" title="c17">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><b> such that </b><br/><a NAME="E7:23_2_1"/><i><font color="Green" title="E20">A49</font></i>: 
( <font color="Maroon" title="c17">M</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c9">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c17">M</font> &amp; <font color="Maroon" title="c12">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c17">M</font> &amp; <font color="Maroon" title="c13">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c17">M</font> )
 <b>by </b><i><a class="txt" href="#E3:23_2_1"><i><font color="Green" title="E18">A47</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><b>consider </b><font color="Maroon" title="c18">N</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><b> such that </b><br/><a NAME="E9:23_2_1"/><i><font color="Green" title="E21">A50</font></i>: 
( <font color="Maroon" title="c18">N</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c9">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">N</font> &amp; <font color="Maroon" title="c14">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">N</font> &amp; <font color="Maroon" title="c15">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">N</font> )
 <b>by </b><i><a class="txt" href="#E3:23_2_1"><i><font color="Green" title="E18">A47</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><a NAME="E10:23_2_1"/><i><font color="Green" title="E22">A51</font></i>: 
( <font color="Maroon" title="c16">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c16">A</font> &amp; <font color="Maroon" title="c17">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c17">M</font> &amp; <font color="Maroon" title="c18">N</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">N</font> )
 <b>by </b><i><a class="txt" href="#E5:23_2_1"><i><font color="Green" title="E19">A48</font></i></a>, <a class="txt" href="#E7:23_2_1"><i><font color="Green" title="E20">A49</font></i></a>, <a class="txt" href="#E9:23_2_1"><i><font color="Green" title="E21">A50</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E11:23_2_1"/><i><font color="Green" title="E23">A52</font></i>: 
( <font color="Maroon" title="c16">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">M</font> &amp; <font color="Maroon" title="c16">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">N</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_2_1_1"/>
(  not <font color="Maroon" title="c16">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">M</font> or  not <font color="Maroon" title="c16">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">N</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="E2:23_2_1_1"/><b>then </b>
( <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="c10">a</font> or <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> )
 
<b>by </b><i><a class="txt" href="#E5:23_2_1"><i><font color="Green" title="E19">A48</font></i></a>, <a class="txt" href="#E7:23_2_1"><i><font color="Green" title="E20">A49</font></i></a>, <a class="txt" href="#E9:23_2_1"><i><font color="Green" title="E21">A50</font></i></a>, <a class="txt" href="#E10:23_2_1"><i><font color="Green" title="E22">A51</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E3:23_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:23_2_1"><i><font color="Green" title="E18">A47</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</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="E12:23_2_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> &amp; <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> )
 <b>by </b><i><a class="txt" href="#E1:23_2_1"><i><font color="Green" title="E17">A46</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E13:23_2_1"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="#E1:23_2"><i><font color="Green" title="E16">A45</font></i></a>, <a class="txt" href="#E1:23_2_1"><i><font color="Green" title="E17">A46</font></i></a>, <a class="txt" href="#E5:23_2_1"><i><font color="Green" title="E19">A48</font></i></a>, <a class="txt" href="#E7:23_2_1"><i><font color="Green" title="E20">A49</font></i></a>, <a class="txt" href="#E9:23_2_1"><i><font color="Green" title="E21">A50</font></i></a>, <a class="txt" href="#E11:23_2_1"><i><font color="Green" title="E23">A52</font></i></a>, <a class="ref" href="aff_2.html#D4" title="AFF_2:def.4">AFF_2:def 4</a></i>;<br/><b>hence </b><a NAME="E14:23_2_1"/>
<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c7">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1'</font>,<font color="Maroon" title="c8">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="E3:23_2"/>
<font color="Maroon" title="c1">X</font> is <a href="conaffm.html#V1" title="CONAFFM:attr.1">satisfying_DES</a>
 <b>by </b><i><a class="ref" href="conaffm.html#D1" title="CONAFFM:def.1">CONAFFM:def 1</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="E3:23"/>
( <font color="Maroon" title="c1">X</font> is <a href="conaffm.html#V1" title="CONAFFM:attr.1">satisfying_DES</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#V4" title="AFF_2:attr.4">Desarguesian</a> )
 <b>by </b><i><a class="txt" href="#E1:23"><i><font color="Green" title="E15">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>
