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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#V5" title="CONAFFM:attr.5">satisfying_LIN</a> implies <font color="Maroon" title="c1">X</font> is <a href="conaffm.html#V6" title="CONAFFM:attr.6">satisfying_LIN1</a> )</span><br/>

<b>assume </b><a NAME="E1:4"/><i><font color="Green" title="E5">A1</font></i>: 
<font color="Maroon" title="c1">X</font> is <a href="conaffm.html#V5" title="CONAFFM:attr.5">satisfying_LIN</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#V6" title="CONAFFM:attr.6">satisfying_LIN1</a></span><br/>

<b>let </b><font color="Maroon" title="c2">o</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="conaffm.html#D6" target="_self" title="CONAFFM:def.6">CONAFFM:def 6</a> <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">a</font>, <font color="Olive" title="b2">a1</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">b1</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">c1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">a</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">c</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">c1</font> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b5">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b6">c1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b1">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b2">a1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b4">b1</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b5">c</font>,<font color="Olive" title="b1">a</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b2">a1</font>,<font color="Olive" title="b4">b1</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b5">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b2">a1</font>,<font color="Olive" title="b6">c1</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">b1</font> holds <br/><font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b4">b1</font>,<font color="Olive" title="b6">c1</font></span><br/><b>let </b><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; <font color="Maroon" title="c3">a</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>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font> &amp; not  <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="c3">a</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="c5">b</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<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="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">b1</font> implies <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font> )</span><br/>













<b>assume </b><a NAME="E2:4"/><i><font color="Green" title="E6">A2</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; <font color="Maroon" title="c3">a</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>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font> &amp; not  <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="c3">a</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="c5">b</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<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="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">b1</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="analmetr.html#R4" title="ANALMETR:pred.4">_|_</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">a'</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c10">a1'</font> = <font color="Maroon" title="c4">a1</font>, <font color="Maroon" title="c11">b'</font> = <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c12">b1'</font> = <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c13">c'</font> = <font color="Maroon" title="c7">c</font>, <font color="Maroon" title="c14">c1'</font> = <font color="Maroon" title="c8">c1</font>, <font color="Maroon" title="c15">o'</font> = <font color="Maroon" title="c2">o</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/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1"><b>now </b></a><div class="add"><a NAME="E1:4_1"/>
 ex <font color="Olive" title="b1">b2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Olive" title="b1">b2</font> &amp; <font color="Maroon" title="c8">c1</font>,<font color="Olive" title="b1">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c8">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">b2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c16">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E2:4_1_1"/><i><font color="Green" title="E7">A3</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">y</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="c16">y</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c17">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E4:4_1_1"/><i><font color="Green" title="E8">A4</font></i>: 
( <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c17">x</font> &amp; <font color="Maroon" title="c8">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">x</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<a NAME="E5:4_1_1"/><i><font color="Green" title="E9">A5</font></i>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c17">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:4_1_1_1"/><i><font color="Green" title="E10">A6</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c17">x</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="c18">y'</font> = <font color="Maroon" title="c16">y</font>, <font color="Maroon" title="c19">x'</font> = <font color="Maroon" title="c17">x</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="E3:4_1_1_1"/><i><font color="Green" title="E11">A7</font></i>: 
<font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c18">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c1'</font>,<font color="Maroon" title="c19">x'</font>
 
<b>by </b><i><a class="txt" href="#E1:4_1_1_1"><i><font color="Green" title="E10">A6</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:4_1_1_1"/>
( <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c10">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c18">y'</font> &amp; <font color="Maroon" title="c15">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">y'</font> )
 
<b>by </b><i><a class="txt" href="#E2:4_1_1"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:4_1_1_1"/><b>then </b>
( <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c18">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c10">a1'</font> &amp; <font color="Maroon" title="c15">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">y'</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="E6:4_1_1_1"/><b>then </b>
<font color="Maroon" title="c14">c1'</font>,<font color="Maroon" title="c19">x'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c10">a1'</font>
 
<b>by </b><i><a class="txt" href="#E3:4_1_1_1"><i><font color="Green" title="E11">A7</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E7:4_1_1_1"/><b>then </b>
<font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c17">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:4_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="#E4:4_1_1"><i><font color="Green" title="E8">A4</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E9:4_1_1_1"/><b>then </b><i><font color="Green" title="E12">A8</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E10:4_1_1_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:4_1_1_1"/><b>then </b>
<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="c2">o</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="#E9:4_1_1_1"><i><font color="Green" title="E12">A8</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E12:4_1_1_1"/><b>then </b>
<font color="Maroon" title="c11">b'</font>,<font color="Maroon" title="c13">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c11">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E13:4_1_1_1"/><b>then </b>
<font color="Maroon" title="c11">b'</font>,<font color="Maroon" title="c13">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">b'</font>,<font color="Maroon" title="c15">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="E14:4_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">b'</font>,<font color="Maroon" title="c13">c'</font>,<font color="Maroon" title="c15">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="E15:4_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c11">b'</font>,<font color="Maroon" title="c13">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="E16:4_1_1_1"/><b>then </b><i><font color="Green" title="E13">A9</font></i>: 
<font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c11">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c13">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="E17:4_1_1_1"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c9">a'</font>,<font color="Maroon" title="c11">b'</font> &amp; <font color="Maroon" title="c15">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">b'</font> )
 
<b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E18:4_1_1_1"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c11">b'</font>,<font color="Maroon" title="c9">a'</font> &amp; <font color="Maroon" title="c15">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">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="E19:4_1_1_1"/><b>then </b>
( <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c11">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c9">a'</font> &amp; <font color="Maroon" title="c15">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">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="E20:4_1_1_1"/><b>then </b>
<font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c13">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c9">a'</font>
 
<b>by </b><i><a class="txt" href="#E16:4_1_1_1"><i><font color="Green" title="E13">A9</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E21:4_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c13">c'</font>,<font color="Maroon" title="c9">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/>
<b>hence </b><a NAME="E22:4_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>reconsider </b><font color="Maroon" title="c18">y'</font> = <font color="Maroon" title="c16">y</font>, <font color="Maroon" title="c19">x'</font> = <font color="Maroon" title="c17">x</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="E7:4_1_1"/>
not <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c18">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c1'</font>,<font color="Maroon" title="c19">x'</font>
 
<b>by </b><i><a class="txt" href="#E5:4_1_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c20">b2'</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><b> such that </b><br/><a NAME="E9:4_1_1"/><i><font color="Green" title="E10">A10</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c18">y'</font>,<font color="Maroon" title="c20">b2'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">c1'</font>,<font color="Maroon" title="c19">x'</font>,<font color="Maroon" title="c20">b2'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c21">b2</font> = <font color="Maroon" title="c20">b2'</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="E11:4_1_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c21">b2</font>
 
<b>by </b><i><a class="txt" href="#E9:4_1_1"><i><font color="Green" title="E10">A10</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:4_1_1"/><b>then </b>
<font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c17">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c21">b2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E13:4_1_1"/><b>then </b><i><font color="Green" title="E11">A11</font></i>: 
<font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c21">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="#E4:4_1_1"><i><font color="Green" title="E8">A4</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E14:4_1_1"/>
( <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c10">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c18">y'</font> &amp; <font color="Maroon" title="c15">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">y'</font> )
 
<b>by </b><i><a class="txt" href="#E2:4_1_1"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E15:4_1_1"/><b>then </b><i><font color="Green" title="E12">A12</font></i>: 
( <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c18">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c10">a1'</font> &amp; <font color="Maroon" title="c15">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">y'</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="E16:4_1_1"/>
<font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c18">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c20">b2'</font>
 
<b>by </b><i><a class="txt" href="#E9:4_1_1"><i><font color="Green" title="E10">A10</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E17:4_1_1"/><b>then </b>
<font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c10">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c20">b2'</font>
 
<b>by </b><i><a class="txt" href="#E15:4_1_1"><i><font color="Green" title="E12">A12</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E18:4_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c10">a1'</font>,<font color="Maroon" title="c20">b2'</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="E19:4_1_1"/><b>then </b><i><font color="Green" title="E13">A13</font></i>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c21">b2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E20:4_1_1"/>
<font color="Maroon" title="c8">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">b2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:4_1_1_2"/>
<font color="Maroon" title="c8">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">b2</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="E2:4_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font>
 
<b>by </b><i><a class="txt" href="#E19:4_1_1"><i><font color="Green" title="E13">A13</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:4_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:4_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<b>hence </b><a NAME="E5:4_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 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>
<b>hence </b><a NAME="E21:4_1_1"/>
 ex <font color="Olive" title="b1">b2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Olive" title="b1">b2</font> &amp; <font color="Maroon" title="c8">c1</font>,<font color="Olive" title="b1">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c8">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">b2</font> )
 <b>by </b><i><a class="txt" href="#E13:4_1_1"><i><font color="Green" title="E11">A11</font></i></a>, <a class="txt" href="#E19:4_1_1"><i><font color="Green" title="E13">A13</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c16">b2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E3:4_1"/><i><font color="Green" title="E7">A14</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c16">b2</font> &amp; <font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c16">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c8">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">b2</font> )
 ;<br/><b>reconsider </b><font color="Maroon" title="c17">b2'</font> = <font color="Maroon" title="c16">b2</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="E5:4_1"/><i><font color="Green" title="E8">A15</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">b2</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="c16">b2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:4_1_2"/><i><font color="Green" title="E9">A16</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">b2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:4_1_2_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">b2</font>
 
<b>by </b><i><a class="txt" href="#E3:4_1"><i><font color="Green" title="E7">A14</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E2:4_1_2_1"/><b>then </b><i><font color="Green" title="E10">A17</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">b2</font>
 
<b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:4_1_2_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E4:4_1_2_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">b2</font>
 <b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="#E2:4_1_2_1"><i><font color="Green" title="E10">A17</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</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="E2:4_1_2"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">b2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:4_1_2_2"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">b2</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="E2:4_1_2_2"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="#E3:4_1"><i><font color="Green" title="E7">A14</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:4_1_2_2"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:4_1_2_2"/><b>then </b>
<font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c13">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">b'</font>,<font color="Maroon" title="c13">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:4_1_2_2"/><b>then </b>
<font color="Maroon" title="c13">c'</font>,<font color="Maroon" title="c15">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">c'</font>,<font color="Maroon" title="c11">b'</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="E6:4_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">c'</font>,<font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c11">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="E7:4_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c11">b'</font>,<font color="Maroon" title="c13">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="E8:4_1_2_2"/><b>then </b><i><font color="Green" title="E10">A18</font></i>: 
<font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c11">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c13">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="E9:4_1_2_2"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c9">a'</font>,<font color="Maroon" title="c11">b'</font> &amp; <font color="Maroon" title="c15">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">b'</font> )
 
<b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:4_1_2_2"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c11">b'</font>,<font color="Maroon" title="c9">a'</font> &amp; <font color="Maroon" title="c15">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">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="E11:4_1_2_2"/><b>then </b>
( <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c11">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c9">a'</font> &amp; <font color="Maroon" title="c15">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">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="E12:4_1_2_2"/><b>then </b>
<font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c13">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c9">a'</font>
 
<b>by </b><i><a class="txt" href="#E8:4_1_2_2"><i><font color="Green" title="E10">A18</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E13:4_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c13">c'</font>,<font color="Maroon" title="c9">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/>
<b>hence </b><a NAME="E14:4_1_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:4_1_2"/>
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">b2</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="c16">b2</font> )
 <b>by </b><i><a class="txt" href="#E1:4_1_2"><i><font color="Green" title="E9">A16</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="E6:4_1"/>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c16">b2</font>,<font color="Maroon" title="c8">c1</font>
 <b>by </b><i><a class="txt" href="#E3:4_1"><i><font color="Green" title="E7">A14</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E7:4_1"/><b>then </b><i><font color="Green" title="E9">A19</font></i>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c16">b2</font>
 <b>by </b><i><a class="txt" href="#E1:4"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="#E3:4_1"><i><font color="Green" title="E7">A14</font></i></a>, <a class="txt" href="#E5:4_1"><i><font color="Green" title="E8">A15</font></i></a>, <a class="ref" href="conaffm.html#D5" target="_self" title="CONAFFM:def.5">Def5</a></i>;<br/><a NAME="E8:4_1"/>
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">b2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:4_1_3"/>
not  <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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:4_1_3_1"/>
 <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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:4_1_3_1"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:4_1_3_1"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>
 
<b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E4:4_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</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="E2:4_1_3"/><b>then </b><i><font color="Green" title="E10">A20</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c9">a'</font>,<font color="Maroon" title="c10">a1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:4_1_3"/><i><font color="Green" title="E11">A21</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c9">a'</font>,<font color="Maroon" title="c11">b'</font>
 
<b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:4_1_3"/><i><font color="Green" title="E12">A22</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c10">a1'</font>,<font color="Maroon" title="c12">b1'</font>
 
<b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:4_1_3"/><i><font color="Green" title="E13">A23</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o'</font>,<font color="Maroon" title="c10">a1'</font>,<font color="Maroon" title="c17">b2'</font>
 
<b>by </b><i><a class="txt" href="#E3:4_1"><i><font color="Green" title="E7">A14</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:4_1_3"/><i><font color="Green" title="E14">A24</font></i>: 
<font color="Maroon" title="c9">a'</font>,<font color="Maroon" title="c10">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">b'</font>,<font color="Maroon" title="c12">b1'</font>
 
<b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:4_1_3"/>
<font color="Maroon" title="c9">a'</font>,<font color="Maroon" title="c10">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">b'</font>,<font color="Maroon" title="c17">b2'</font>
 
<b>by </b><i><a class="txt" href="#E7:4_1"><i><font color="Green" title="E9">A19</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E8:4_1_3"/>
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">b2</font>
 <b>by </b><i><a class="txt" href="#E2:4_1_3"><i><font color="Green" title="E10">A20</font></i></a>, <a class="txt" href="#E3:4_1_3"><i><font color="Green" title="E11">A21</font></i></a>, <a class="txt" href="#E4:4_1_3"><i><font color="Green" title="E12">A22</font></i></a>, <a class="txt" href="#E5:4_1_3"><i><font color="Green" title="E13">A23</font></i></a>, <a class="txt" href="#E6:4_1_3"><i><font color="Green" title="E14">A24</font></i></a>, <a class="ref" href="aff_1.html#T70" title="AFF_1:th.70">AFF_1:70</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="E9:4_1"/>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font>
 <b>by </b><i><a class="txt" href="#E3:4_1"><i><font color="Green" title="E7">A14</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</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="E5:4"/>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</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"> verum</span><br/>


</div>
