<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c7">POS</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="c7">POS</font> is   <a href="analmetr.html#NM1" title="ANALMETR:NM.1">OrtAfSp</a></span><br/>

<a NAME="E1:61"/><i><font color="Green" title="E49">A1</font></i>: 
 <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analoaf.html#G1" title="ANALOAF:aggr.1">AffinStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">POS</font>,the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #)
 
;<br/>
<a NAME="E2:61"/><i><font color="Green" title="E50">A2</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font>  ex <font color="Olive" title="b4">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">x</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">x</font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#D10" target="_self" title="ANALMETR:def.10">Def10</a></i>;<br/>
<a NAME="E3:61"/><i><font color="Green" title="E51">A3</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">q</font>, <font color="Olive" title="b7">r</font>, <font color="Olive" title="b8">s</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b8">s</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b6">q</font>,<font color="Olive" title="b8">s</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c9">b</font>, <font color="Maroon" title="c10">c</font>, <font color="Maroon" title="c11">d</font>, <font color="Maroon" title="c12">p</font>, <font color="Maroon" title="c13">q</font>, <font color="Maroon" title="c14">r</font>, <font color="Maroon" title="c15">s</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> &amp; <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c15">s</font> implies <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c15">s</font> )</span><br/>

<b>assume </b><a NAME="E1:61_1"/><i><font color="Green" title="E52">A4</font></i>: 
( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> &amp; <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c15">s</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c15">s</font></span><br/>

<div><i><font color="Green" title="E53">A5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:61_1_1"/>
<font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c15">s</font></span><br/><a NAME="E2:61_1_1"/><b>then </b>
<font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c15">s</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D10" target="_self" title="ANALMETR:def.10">Def10</a></i>;<br/><b>hence </b><a NAME="E3:61_1_1"/>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c15">s</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D10" target="_self" title="ANALMETR:def.10">Def10</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="61_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:61_1_2"/><i><font color="Green" title="E54">A6</font></i>: 
( <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b</font> &amp; <font color="Maroon" title="c12">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">q</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c15">s</font></span><br/><a NAME="E2:61_1_2"/><b>then </b><i><font color="Green" title="E55">A7</font></i>: 
<font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c15">s</font>
 <b>by </b><i><a class="txt" href="#E1:61_1"><i><font color="Green" title="E52">A4</font></i></a>, <a class="ref" href="analmetr.html#D10" target="_self" title="ANALMETR:def.10">Def10</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c16">p'</font> = <font color="Maroon" title="c12">p</font>, <font color="Maroon" title="c17">q'</font> = <font color="Maroon" title="c13">q</font>, <font color="Maroon" title="c18">s'</font> = <font color="Maroon" title="c15">s</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="c7">POS</font></span>)</span> ;<br/><a NAME="E4:61_1_2"/><i><font color="Green" title="E56">A8</font></i>: 
<font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 <b>by </b><i><a class="txt" href="#E1:61_1"><i><font color="Green" title="E52">A4</font></i></a>, <a class="ref" href="analmetr.html#D10" target="_self" title="ANALMETR:def.10">Def10</a></i>;<br/><a NAME="E5:61_1_2"/>
<font color="Maroon" title="c16">p'</font>,<font color="Maroon" title="c17">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">p'</font>,<font color="Maroon" title="c18">s'</font>
 <b>by </b><i><a class="txt" href="#E2:61_1_2"><i><font color="Green" title="E55">A7</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/><a NAME="E6:61_1_2"/><b>then </b>
<font color="Maroon" title="c17">q'</font>,<font color="Maroon" title="c16">p'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">q'</font>,<font color="Maroon" title="c18">s'</font>
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E7:61_1_2"/><b>then </b>
<font color="Maroon" title="c16">p'</font>,<font color="Maroon" title="c17">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">q'</font>,<font color="Maroon" title="c18">s'</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="E8:61_1_2"/><b>then </b>
<font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c15">s</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/><b>hence </b><a NAME="E9:61_1_2"/>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c15">s</font>
 <b>by </b><i><a class="txt" href="#E1:61_1_2"><i><font color="Green" title="E54">A6</font></i></a>, <a class="txt" href="#E4:61_1_2"><i><font color="Green" title="E56">A8</font></i></a>, <a class="ref" href="analmetr.html#D10" target="_self" title="ANALMETR:def.10">Def10</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="E4:61_1"/>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c15">s</font>
 <b>by </b><i><a class="txt" href="#E1:61_1"><i><font color="Green" title="E52">A4</font></i></a>, <a class="txt" href="#E2:61_1"><i><font color="Green" title="E53">A5</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="E4:61"/><i><font color="Green" title="E52">A9</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> holds <br/> ex <font color="Olive" title="b4">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">x</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b4">x</font>,<font color="Olive" title="b3">c</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c9">b</font>, <font color="Maroon" title="c10">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b</font> implies  ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c10">c</font> ) )</span><br/>

<b>assume </b><a NAME="E1:61_2"/><i><font color="Green" title="E53">A10</font></i>: 
<font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c10">c</font> )</span><br/>

<b>consider </b><font color="Maroon" title="c11">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font><b> such that </b><br/><a NAME="E3:61_2"/><i><font color="Green" title="E54">A11</font></i>: 
( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c11">y</font> &amp; <font color="Maroon" title="c10">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">y</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10" target="_self" title="ANALMETR:def.10">Def10</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">a'</font> = <font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c13">b'</font> = <font color="Maroon" title="c9">b</font>, <font color="Maroon" title="c14">c'</font> = <font color="Maroon" title="c10">c</font>, <font color="Maroon" title="c15">y'</font> = <font color="Maroon" title="c11">y</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="c7">POS</font></span>)</span> ;<br/>
<a NAME="E5:61_2"/>
not <font color="Maroon" title="c12">a'</font>,<font color="Maroon" title="c13">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c'</font>,<font color="Maroon" title="c15">y'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:61_2_1"/>
<font color="Maroon" title="c12">a'</font>,<font color="Maroon" title="c13">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c'</font>,<font color="Maroon" title="c15">y'</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="E2:61_2_1"/><b>then </b>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c11">y</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/>
<a NAME="E3:61_2_1"/><b>then </b>
<font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c11">y</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c11">y</font>
 
<b>by </b><i><a class="txt" href="#E1:61_2"><i><font color="Green" title="E53">A10</font></i></a>, <a class="txt" href="#E3:61_2"><i><font color="Green" title="E54">A11</font></i></a>, <a class="ref" href="analmetr.html#D10" target="_self" title="ANALMETR:def.10">Def10</a></i>;<br/>
<b>hence </b><a NAME="E4:61_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:61_2"><i><font color="Green" title="E54">A11</font></i></a>, <a class="ref" href="analmetr.html#D10" target="_self" title="ANALMETR:def.10">Def10</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">x'</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="c7">POS</font></span>)</span><b> such that </b><br/><a NAME="E7:61_2"/><i><font color="Green" title="E55">A12</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a'</font>,<font color="Maroon" title="c13">b'</font>,<font color="Maroon" title="c16">x'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">c'</font>,<font color="Maroon" title="c15">y'</font>,<font color="Maroon" title="c16">x'</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="c17">x</font> = <font color="Maroon" title="c16">x'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> ;<br/>
<a NAME="E9:61_2"/>
( <font color="Maroon" title="c12">a'</font>,<font color="Maroon" title="c13">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a'</font>,<font color="Maroon" title="c16">x'</font> &amp; <font color="Maroon" title="c14">c'</font>,<font color="Maroon" title="c15">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c'</font>,<font color="Maroon" title="c16">x'</font> )
 
<b>by </b><i><a class="txt" href="#E7:61_2"><i><font color="Green" title="E55">A12</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="E10:61_2"/><b>then </b><i><font color="Green" title="E56">A13</font></i>: 
( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c17">x</font> &amp; <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c11">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c17">x</font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/>
<a NAME="E11:61_2"/>
<font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c11">y</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<b>by </b><i><a class="txt" href="#E3:61_2"><i><font color="Green" title="E54">A11</font></i></a>, <a class="ref" href="analmetr.html#D10" target="_self" title="ANALMETR:def.10">Def10</a></i>;<br/>
<a NAME="E12:61_2"/><b>then </b>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c17">x</font>
 
<b>by </b><i><a class="txt" href="#E3:61_2"><i><font color="Green" title="E54">A11</font></i></a>, <a class="txt" href="#E10:61_2"><i><font color="Green" title="E56">A13</font></i></a>, <a class="ref" href="analmetr.html#D10" target="_self" title="ANALMETR:def.10">Def10</a></i>;<br/>
<a NAME="E13:61_2"/><b>then </b>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c10">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D10" target="_self" title="ANALMETR:def.10">Def10</a></i>;<br/>
<b>hence </b><a NAME="E14:61_2"/>
 ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c10">c</font> )
 <b>by </b><i><a class="txt" href="#E10:61_2"><i><font color="Green" title="E56">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>
<a NAME="E5:61"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">q</font>, <font color="Olive" title="b7">r</font>, <font color="Olive" title="b8">s</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> holds <br/> ( ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> implies <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> ) &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b3">c</font> &amp; ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> implies ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b4">d</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> ) ) &amp; ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b7">r</font>,<font color="Olive" title="b8">s</font> &amp; not <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b7">r</font>,<font color="Olive" title="b8">s</font> implies <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> ) &amp; ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b8">s</font> implies <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b6">q</font>,<font color="Olive" title="b8">s</font> ) )
 
<b>by </b><i><a class="txt" href="#E3:61"><i><font color="Green" title="E51">A3</font></i></a>, <a class="ref" href="analmetr.html#D10" target="_self" title="ANALMETR:def.10">Def10</a></i>;<br/>
<b>hence </b><a NAME="E6:61"/>
<font color="Maroon" title="c7">POS</font> is   <a href="analmetr.html#NM1" title="ANALMETR:NM.1">OrtAfSp</a>
 <b>by </b><i><a class="txt" href="#E1:61"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="#E2:61"><i><font color="Green" title="E50">A2</font></i></a>, <a class="txt" href="#E4:61"><i><font color="Green" title="E52">A9</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</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>
