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

<b>assume </b><a NAME="E1:63"/><i><font color="Green" title="E51">A1</font></i>: 
 <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font> is   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a>
 ;<br/>

<a NAME="E2:63"/><i><font color="Green" title="E52">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="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="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#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>now </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>;<br/><b>thus </b><a NAME="E1:63_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="c8">a</font>,<font color="Maroon" title="c9">b</font> implies <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b</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="c10">c</font>,<font color="Maroon" title="c10">c</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="c10">c</font>,<font color="Maroon" title="c11">d</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="c11">d</font>,<font color="Maroon" title="c10">c</font> &amp; <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c11">d</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> ) ) &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="c13">q</font> &amp; <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="c14">r</font>,<font color="Maroon" title="c15">s</font> &amp; not <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="c14">r</font>,<font color="Maroon" title="c15">s</font> implies <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b</font> ) )
 <b>by </b><i><a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><b>thus </b><a NAME="E2:63_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="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="c14">r</font>,<font color="Maroon" title="c15">s</font> &amp; not <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="c14">r</font>,<font color="Maroon" title="c15">s</font> implies <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:63_1_1"/><i><font color="Green" title="E53">A3</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="c14">r</font>,<font color="Maroon" title="c15">s</font> )
 ;<br/>

<b>assume </b><a NAME="E2:63_1_1"/><i><font color="Green" title="E54">A4</font></i>: 
( not <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="c14">r</font>,<font color="Maroon" title="c15">s</font> &amp; not <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c16">a'</font> = <font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c17">b'</font> = <font color="Maroon" title="c9">b</font>, <font color="Maroon" title="c18">p'</font> = <font color="Maroon" title="c12">p</font>, <font color="Maroon" title="c19">q'</font> = <font color="Maroon" title="c13">q</font>, <font color="Maroon" title="c20">r'</font> = <font color="Maroon" title="c14">r</font>, <font color="Maroon" title="c21">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="E4:63_1_1"/><i><font color="Green" title="E55">A5</font></i>: 
not <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E2:63_1_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/>
<a NAME="E5:63_1_1"/><b>then </b><i><font color="Green" title="E56">A6</font></i>: 
( <font color="Maroon" title="c18">p'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">q'</font> &amp; <font color="Maroon" title="c20">r'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">s'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T12" title="AFF_1:th.12">AFF_1:12</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c22">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="E7:63_1_1"/><i><font color="Green" title="E57">A7</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c22">x'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font>,<font color="Maroon" title="c22">x'</font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E1:63"><i><font color="Green" title="E51">A1</font></i></a>, <a class="txt" href="analmetr.html#E4:63_1_1"><i><font color="Green" title="E55">A5</font></i></a>, <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="c23">x</font> = <font color="Maroon" title="c22">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="E9:63_1_1"/><i><font color="Green" title="E58">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> &amp; <font color="Maroon" title="c14">r</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="txt" href="analmetr.html#E1:63_1_1"><i><font color="Green" title="E53">A3</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>
<a NAME="E10:63_1_1"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c22">x'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">s'</font>,<font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c22">x'</font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E7:63_1_1"><i><font color="Green" title="E57">A7</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E11:63_1_1"/><b>then </b>
( <font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c18">p'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c22">x'</font> &amp; <font color="Maroon" title="c21">s'</font>,<font color="Maroon" title="c20">r'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">s'</font>,<font color="Maroon" title="c22">x'</font> &amp; <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c22">x'</font> &amp; <font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c22">x'</font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E7:63_1_1"><i><font color="Green" title="E57">A7</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="E12:63_1_1"/><b>then </b><i><font color="Green" title="E59">A9</font></i>: 
( <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c19">q'</font> &amp; <font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font> &amp; <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c18">p'</font> &amp; <font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</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="E13:63_1_1"/><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="c23">x</font>,<font color="Maroon" title="c13">q</font> &amp; <font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c15">s</font> &amp; <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="c23">x</font>,<font color="Maroon" title="c12">p</font> &amp; <font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c14">r</font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/>
<a NAME="E14:63_1_1"/><b>then </b><i><font color="Green" title="E60">A10</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="c23">x</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="c23">x</font>,<font color="Maroon" title="c12">p</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="c23">x</font>,<font color="Maroon" title="c14">r</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="c23">x</font>,<font color="Maroon" title="c15">s</font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E5:63_1_1"><i><font color="Green" title="E56">A6</font></i></a>, <a class="txt" href="analmetr.html#E9:63_1_1"><i><font color="Green" title="E58">A8</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>
<a NAME="E15:63_1_1"/><b>then </b><i><font color="Green" title="E61">A11</font></i>: 
( <font color="Maroon" title="c23">x</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> &amp; <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c12">p</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> &amp; <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c14">r</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> &amp; <font color="Maroon" title="c23">x</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#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>
<div><i><font color="Green" title="E62">A12</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_1_1_1"/><i><font color="Green" title="E63">A13</font></i>: 
( <font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">p</font> &amp; <font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">r</font> )
 ;<br/><b>consider </b><font color="Maroon" title="c24">y'</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="E3:63_1_1_1"/><i><font color="Green" title="E64">A14</font></i>: 
( <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c24">y'</font> &amp; <font color="Maroon" title="c18">p'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">y'</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E4:63_1_1_1"/>
not <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c24">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:63_1_1_1_1"/>
<font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c24">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font>
 ;<br/>

<a NAME="E2:63_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c24">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E12:63_1_1"><i><font color="Green" title="E59">A9</font></i></a>, <a class="txt" href="analmetr.html#E1:63_1_1_1"><i><font color="Green" title="E63">A13</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:63_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">b'</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E3:63_1_1_1"><i><font color="Green" title="E64">A14</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E4:63_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/>
<a NAME="E5:63_1_1_1_1"/><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="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E5:63_1_1"><i><font color="Green" title="E56">A6</font></i></a>, <a class="txt" href="analmetr.html#E9:63_1_1"><i><font color="Green" title="E58">A8</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>
<b>hence </b><a NAME="E6:63_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="analmetr.html#E2:63_1_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c25">z'</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="E6:63_1_1_1"/><i><font color="Green" title="E65">A15</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c24">y'</font>,<font color="Maroon" title="c25">z'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c25">z'</font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E1:63"><i><font color="Green" title="E51">A1</font></i></a>, <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="c26">z</font> = <font color="Maroon" title="c25">z'</font> as    <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> ;<br/><a NAME="E8:63_1_1_1"/><i><font color="Green" title="E66">A16</font></i>: 
( <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c24">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c25">z'</font> &amp; <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c25">z'</font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E6:63_1_1_1"><i><font color="Green" title="E65">A15</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="E9:63_1_1_1"/><b>then </b>
<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c25">z'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E3:63_1_1_1"><i><font color="Green" title="E64">A14</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E10:63_1_1_1"/><b>then </b><i><font color="Green" title="E67">A17</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="c12">p</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/><a NAME="E11:63_1_1_1"/>
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c14">r</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E8:63_1_1_1"><i><font color="Green" title="E66">A16</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/><a NAME="E12:63_1_1_1"/><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="c23">x</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E15:63_1_1"><i><font color="Green" title="E61">A11</font></i></a>, <a class="txt" href="analmetr.html#E1:63_1_1_1"><i><font color="Green" title="E63">A13</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><a NAME="E13:63_1_1_1"/><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="c12">p</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E14:63_1_1"><i><font color="Green" title="E60">A10</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><a NAME="E14:63_1_1_1"/><b>then </b>
<font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c26">z</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E2:63_1_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="txt" href="analmetr.html#E10:63_1_1_1"><i><font color="Green" title="E67">A17</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><a NAME="E15:63_1_1_1"/><b>then </b>
<font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c18">p'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E8:63_1_1_1"><i><font color="Green" title="E66">A16</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><a NAME="E16:63_1_1_1"/><b>then </b><i><font color="Green" title="E68">A18</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c18">p'</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="E17:63_1_1_1"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c22">x'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E7:63_1_1"><i><font color="Green" title="E57">A7</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/><a NAME="E18:63_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c19">q'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E1:63_1_1_1"><i><font color="Green" title="E63">A13</font></i></a>, <a class="txt" href="analmetr.html#E16:63_1_1_1"><i><font color="Green" title="E68">A18</font></i></a>, <a class="ref" href="aff_1.html#T20" title="AFF_1:th.20">AFF_1:20</a></i>;<br/><a NAME="E19:63_1_1_1"/><b>then </b>
<font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E16:63_1_1_1"><i><font color="Green" title="E68">A18</font></i></a>, <a class="ref" href="aff_1.html#T19" title="AFF_1:th.19">AFF_1:19</a></i>;<br/><a NAME="E20:63_1_1_1"/><b>then </b>
<font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E12:63_1_1"><i><font color="Green" title="E59">A9</font></i></a>, <a class="txt" href="analmetr.html#E1:63_1_1_1"><i><font color="Green" title="E63">A13</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><b>hence </b><a NAME="E21:63_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="analmetr.html#E2:63_1_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E63">A19</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_1_1_2"/><i><font color="Green" title="E64">A20</font></i>: 
( <font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">p</font> &amp; <font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">s</font> )
 ;<br/><b>consider </b><font color="Maroon" title="c24">y'</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="E3:63_1_1_2"/><i><font color="Green" title="E65">A21</font></i>: 
( <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c24">y'</font> &amp; <font color="Maroon" title="c18">p'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">y'</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E4:63_1_1_2"/>
not <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c24">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:63_1_1_2_1"/>
<font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c24">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font>
 ;<br/>

<a NAME="E2:63_1_1_2_1"/><b>then </b>
<font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c24">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E12:63_1_1"><i><font color="Green" title="E59">A9</font></i></a>, <a class="txt" href="analmetr.html#E1:63_1_1_2"><i><font color="Green" title="E64">A20</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:63_1_1_2_1"/><b>then </b>
<font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">b'</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E3:63_1_1_2"><i><font color="Green" title="E65">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="E4:63_1_1_2_1"/><b>then </b>
<font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/>
<a NAME="E5:63_1_1_2_1"/><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="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E5:63_1_1"><i><font color="Green" title="E56">A6</font></i></a>, <a class="txt" href="analmetr.html#E9:63_1_1"><i><font color="Green" title="E58">A8</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>
<b>hence </b><a NAME="E6:63_1_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="analmetr.html#E2:63_1_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c25">z'</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="E6:63_1_1_2"/><i><font color="Green" title="E66">A22</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c24">y'</font>,<font color="Maroon" title="c25">z'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font>,<font color="Maroon" title="c25">z'</font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E1:63"><i><font color="Green" title="E51">A1</font></i></a>, <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="c26">z</font> = <font color="Maroon" title="c25">z'</font> as    <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> ;<br/><a NAME="E8:63_1_1_2"/><i><font color="Green" title="E67">A23</font></i>: 
( <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c24">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c25">z'</font> &amp; <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c25">z'</font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E6:63_1_1_2"><i><font color="Green" title="E66">A22</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="E9:63_1_1_2"/><b>then </b>
<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c25">z'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E3:63_1_1_2"><i><font color="Green" title="E65">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="E10:63_1_1_2"/><b>then </b><i><font color="Green" title="E68">A24</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="c12">p</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/><a NAME="E11:63_1_1_2"/>
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c15">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E8:63_1_1_2"><i><font color="Green" title="E67">A23</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/><a NAME="E12:63_1_1_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="c23">x</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E15:63_1_1"><i><font color="Green" title="E61">A11</font></i></a>, <a class="txt" href="analmetr.html#E1:63_1_1_2"><i><font color="Green" title="E64">A20</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><a NAME="E13:63_1_1_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="c12">p</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E14:63_1_1"><i><font color="Green" title="E60">A10</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><a NAME="E14:63_1_1_2"/><b>then </b>
<font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c26">z</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E2:63_1_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="txt" href="analmetr.html#E10:63_1_1_2"><i><font color="Green" title="E68">A24</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><a NAME="E15:63_1_1_2"/><b>then </b>
<font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c18">p'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E8:63_1_1_2"><i><font color="Green" title="E67">A23</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><a NAME="E16:63_1_1_2"/><b>then </b><i><font color="Green" title="E69">A25</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font>,<font color="Maroon" title="c18">p'</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="E17:63_1_1_2"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font>,<font color="Maroon" title="c22">x'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E7:63_1_1"><i><font color="Green" title="E57">A7</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/><a NAME="E18:63_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font>,<font color="Maroon" title="c19">q'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E1:63_1_1_2"><i><font color="Green" title="E64">A20</font></i></a>, <a class="txt" href="analmetr.html#E16:63_1_1_2"><i><font color="Green" title="E69">A25</font></i></a>, <a class="ref" href="aff_1.html#T20" title="AFF_1:th.20">AFF_1:20</a></i>;<br/><a NAME="E19:63_1_1_2"/><b>then </b>
<font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E16:63_1_1_2"><i><font color="Green" title="E69">A25</font></i></a>, <a class="ref" href="aff_1.html#T19" title="AFF_1:th.19">AFF_1:19</a></i>;<br/><a NAME="E20:63_1_1_2"/><b>then </b>
<font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E12:63_1_1"><i><font color="Green" title="E59">A9</font></i></a>, <a class="txt" href="analmetr.html#E1:63_1_1_2"><i><font color="Green" title="E64">A20</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><b>hence </b><a NAME="E21:63_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="analmetr.html#E2:63_1_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E64">A26</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_1_1_3"/><i><font color="Green" title="E65">A27</font></i>: 
( <font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">q</font> &amp; <font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">r</font> )
 ;<br/><b>consider </b><font color="Maroon" title="c24">y'</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="E3:63_1_1_3"/><i><font color="Green" title="E66">A28</font></i>: 
( <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c24">y'</font> &amp; <font color="Maroon" title="c19">q'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">y'</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E4:63_1_1_3"/>
not <font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c24">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:63_1_1_3_1"/>
<font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c24">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font>
 ;<br/>

<a NAME="E2:63_1_1_3_1"/><b>then </b>
<font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c24">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E12:63_1_1"><i><font color="Green" title="E59">A9</font></i></a>, <a class="txt" href="analmetr.html#E1:63_1_1_3"><i><font color="Green" title="E65">A27</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:63_1_1_3_1"/><b>then </b>
<font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">b'</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E3:63_1_1_3"><i><font color="Green" title="E66">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="E4:63_1_1_3_1"/><b>then </b>
<font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/>
<a NAME="E5:63_1_1_3_1"/><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="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E5:63_1_1"><i><font color="Green" title="E56">A6</font></i></a>, <a class="txt" href="analmetr.html#E9:63_1_1"><i><font color="Green" title="E58">A8</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>
<b>hence </b><a NAME="E6:63_1_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="analmetr.html#E2:63_1_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c25">z'</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="E6:63_1_1_3"/><i><font color="Green" title="E67">A29</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c24">y'</font>,<font color="Maroon" title="c25">z'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c25">z'</font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E1:63"><i><font color="Green" title="E51">A1</font></i></a>, <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="c26">z</font> = <font color="Maroon" title="c25">z'</font> as    <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> ;<br/><a NAME="E8:63_1_1_3"/><i><font color="Green" title="E68">A30</font></i>: 
( <font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c24">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c25">z'</font> &amp; <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c25">z'</font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E6:63_1_1_3"><i><font color="Green" title="E67">A29</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="E9:63_1_1_3"/><b>then </b>
<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c25">z'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E3:63_1_1_3"><i><font color="Green" title="E66">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="E10:63_1_1_3"/><b>then </b><i><font color="Green" title="E69">A31</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="c13">q</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/><a NAME="E11:63_1_1_3"/>
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c14">r</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E8:63_1_1_3"><i><font color="Green" title="E68">A30</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/><a NAME="E12:63_1_1_3"/><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="c23">x</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E15:63_1_1"><i><font color="Green" title="E61">A11</font></i></a>, <a class="txt" href="analmetr.html#E1:63_1_1_3"><i><font color="Green" title="E65">A27</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><a NAME="E13:63_1_1_3"/><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="c13">q</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E14:63_1_1"><i><font color="Green" title="E60">A10</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><a NAME="E14:63_1_1_3"/><b>then </b>
<font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c26">z</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E2:63_1_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="txt" href="analmetr.html#E10:63_1_1_3"><i><font color="Green" title="E69">A31</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><a NAME="E15:63_1_1_3"/><b>then </b>
<font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c19">q'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E8:63_1_1_3"><i><font color="Green" title="E68">A30</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><a NAME="E16:63_1_1_3"/><b>then </b><i><font color="Green" title="E70">A32</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c19">q'</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="E17:63_1_1_3"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c22">x'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c18">p'</font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E7:63_1_1"><i><font color="Green" title="E57">A7</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/><a NAME="E18:63_1_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c18">p'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E1:63_1_1_3"><i><font color="Green" title="E65">A27</font></i></a>, <a class="txt" href="analmetr.html#E16:63_1_1_3"><i><font color="Green" title="E70">A32</font></i></a>, <a class="ref" href="aff_1.html#T20" title="AFF_1:th.20">AFF_1:20</a></i>;<br/><a NAME="E19:63_1_1_3"/><b>then </b>
<font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c20">r'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E16:63_1_1_3"><i><font color="Green" title="E70">A32</font></i></a>, <a class="ref" href="aff_1.html#T19" title="AFF_1:th.19">AFF_1:19</a></i>;<br/><a NAME="E20:63_1_1_3"/><b>then </b>
<font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E12:63_1_1"><i><font color="Green" title="E59">A9</font></i></a>, <a class="txt" href="analmetr.html#E1:63_1_1_3"><i><font color="Green" title="E65">A27</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><b>hence </b><a NAME="E21:63_1_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="analmetr.html#E2:63_1_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_1_1_4"/><i><font color="Green" title="E65">A33</font></i>: 
( <font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">q</font> &amp; <font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">s</font> )
 ;<br/><b>consider </b><font color="Maroon" title="c24">y'</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="E3:63_1_1_4"/><i><font color="Green" title="E66">A34</font></i>: 
( <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c24">y'</font> &amp; <font color="Maroon" title="c19">q'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">y'</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E4:63_1_1_4"/>
not <font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c24">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:63_1_1_4_1"/>
<font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c24">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font>
 ;<br/>

<a NAME="E2:63_1_1_4_1"/><b>then </b>
<font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c24">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E12:63_1_1"><i><font color="Green" title="E59">A9</font></i></a>, <a class="txt" href="analmetr.html#E1:63_1_1_4"><i><font color="Green" title="E65">A33</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:63_1_1_4_1"/><b>then </b>
<font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">b'</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E3:63_1_1_4"><i><font color="Green" title="E66">A34</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E4:63_1_1_4_1"/><b>then </b>
<font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/>
<a NAME="E5:63_1_1_4_1"/><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="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E5:63_1_1"><i><font color="Green" title="E56">A6</font></i></a>, <a class="txt" href="analmetr.html#E9:63_1_1"><i><font color="Green" title="E58">A8</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>
<b>hence </b><a NAME="E6:63_1_1_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="analmetr.html#E2:63_1_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c25">z'</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="E6:63_1_1_4"/><i><font color="Green" title="E67">A35</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c24">y'</font>,<font color="Maroon" title="c25">z'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font>,<font color="Maroon" title="c25">z'</font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E1:63"><i><font color="Green" title="E51">A1</font></i></a>, <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="c26">z</font> = <font color="Maroon" title="c25">z'</font> as    <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> ;<br/><a NAME="E8:63_1_1_4"/><i><font color="Green" title="E68">A36</font></i>: 
( <font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c24">y'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c25">z'</font> &amp; <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c25">z'</font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E6:63_1_1_4"><i><font color="Green" title="E67">A35</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="E9:63_1_1_4"/><b>then </b>
<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c25">z'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E3:63_1_1_4"><i><font color="Green" title="E66">A34</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E10:63_1_1_4"/><b>then </b><i><font color="Green" title="E69">A37</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="c13">q</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/><a NAME="E11:63_1_1_4"/>
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c15">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E8:63_1_1_4"><i><font color="Green" title="E68">A36</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/><a NAME="E12:63_1_1_4"/><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="c23">x</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E15:63_1_1"><i><font color="Green" title="E61">A11</font></i></a>, <a class="txt" href="analmetr.html#E1:63_1_1_4"><i><font color="Green" title="E65">A33</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><a NAME="E13:63_1_1_4"/><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="c13">q</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E14:63_1_1"><i><font color="Green" title="E60">A10</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><a NAME="E14:63_1_1_4"/><b>then </b>
<font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c26">z</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c26">z</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E2:63_1_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="txt" href="analmetr.html#E10:63_1_1_4"><i><font color="Green" title="E69">A37</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><a NAME="E15:63_1_1_4"/><b>then </b>
<font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c19">q'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E8:63_1_1_4"><i><font color="Green" title="E68">A36</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/><a NAME="E16:63_1_1_4"/><b>then </b><i><font color="Green" title="E70">A38</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font>,<font color="Maroon" title="c19">q'</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="E17:63_1_1_4"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font>,<font color="Maroon" title="c22">x'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c19">q'</font>,<font color="Maroon" title="c18">p'</font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E7:63_1_1"><i><font color="Green" title="E57">A7</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/><a NAME="E18:63_1_1_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font>,<font color="Maroon" title="c18">p'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E1:63_1_1_4"><i><font color="Green" title="E65">A33</font></i></a>, <a class="txt" href="analmetr.html#E16:63_1_1_4"><i><font color="Green" title="E70">A38</font></i></a>, <a class="ref" href="aff_1.html#T20" title="AFF_1:th.20">AFF_1:20</a></i>;<br/><a NAME="E19:63_1_1_4"/><b>then </b>
<font color="Maroon" title="c22">x'</font>,<font color="Maroon" title="c21">s'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E16:63_1_1_4"><i><font color="Green" title="E70">A38</font></i></a>, <a class="ref" href="aff_1.html#T19" title="AFF_1:th.19">AFF_1:19</a></i>;<br/><a NAME="E20:63_1_1_4"/><b>then </b>
<font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r'</font>,<font color="Maroon" title="c21">s'</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E12:63_1_1"><i><font color="Green" title="E59">A9</font></i></a>, <a class="txt" href="analmetr.html#E1:63_1_1_4"><i><font color="Green" title="E65">A33</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><b>hence </b><a NAME="E21:63_1_1_4"/>
contradiction
 <b>by </b><i><a class="txt" href="analmetr.html#E2:63_1_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E20:63_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="analmetr.html#E4:63_1_1"><i><font color="Green" title="E55">A5</font></i></a>, <a class="txt" href="analmetr.html#E16:63_1_1"><i><font color="Green" title="E62">A12</font></i></a>, <a class="txt" href="analmetr.html#E17:63_1_1"><i><font color="Green" title="E63">A19</font></i></a>, <a class="txt" href="analmetr.html#E18:63_1_1"><i><font color="Green" title="E64">A26</font></i></a>, <a class="ref" href="aff_1.html#T12" title="AFF_1:th.12">AFF_1:12</a></i>;<br/>


</div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:63"/>
<font color="Maroon" title="c7">POS</font> is   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>
 <b>by </b><i><a class="txt" href="analmetr.html#E1:63"><i><font color="Green" title="E51">A1</font></i></a>, <a class="txt" href="analmetr.html#E2:63"><i><font color="Green" title="E52">A2</font></i></a>, <a class="ref" href="analmetr.html#D10" target="_self" title="ANALMETR:def.10">Def10</a></i>;<br/>


</div>
