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

<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:15"/><i><font color="Green" title="E15">A1</font></i>: 
 <a href="conmetr.html#NR1" title="CONMETR:NR.1">OPAP_holds_in</a> <font color="Maroon" title="c1">X</font>
 <b>and </b><br/><a NAME="E2:15"/><i><font color="Green" title="E16">A2</font></i>: 
 <a href="conaffm.html#NR1" title="CONAFFM:NR.1">DES_holds_in</a> <font color="Maroon" title="c1">X</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">o</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="conmetr.html#D2" target="_self" title="CONMETR:def.2">CONMETR:def 2</a><br/><b>let </b><font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c4">a2</font>, <font color="Maroon" title="c5">a3</font>, <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c8">b3</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c9">M</font>, <font color="Maroon" title="c10">N</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/>

















<b>assume </b><b>that </b><br/><a NAME="E3:15"/><i><font color="Green" title="E17">A3</font></i>: 
( <font color="Maroon" title="c9">M</font> <a href="analmetr.html#NR6" title="ANALMETR:NR.6">is_line</a>  &amp; <font color="Maroon" title="c10">N</font> <a href="analmetr.html#NR6" title="ANALMETR:NR.6">is_line</a>  )
 <b>and </b><br/><a NAME="E4:15"/><i><font color="Green" title="E18">A4</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font> &amp; <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font> &amp; <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font> &amp; <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font> &amp; not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font> &amp; not <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c11">o'</font> = <font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c12">a1'</font> = <font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c13">a2'</font> = <font color="Maroon" title="c4">a2</font>, <font color="Maroon" title="c14">a3'</font> = <font color="Maroon" title="c5">a3</font>, <font color="Maroon" title="c15">b1'</font> = <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c16">b2'</font> = <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c17">b3'</font> = <font color="Maroon" title="c8">b3</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c18">M'</font> = <font color="Maroon" title="c9">M</font>, <font color="Maroon" title="c19">N'</font> = <font color="Maroon" title="c10">N</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></i>;<br/>
<a NAME="E7:15"/><i><font color="Green" title="E19">A5</font></i>: 
( <font color="Maroon" title="c18">M'</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c19">N'</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  )
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="analmetr.html#T58" title="ANALMETR:th.58">ANALMETR:58</a></i>;<br/>
<a NAME="E8:15"/><b>then </b><i><font color="Green" title="E20">A6</font></i>: 
( <font color="Maroon" title="c18">M'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font> &amp; <font color="Maroon" title="c19">N'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c19">N'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1"/><i><font color="Green" title="E21">A7</font></i>: 
not <font color="Maroon" title="c9">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c10">N</font>
 ;<br/><div><i><font color="Green" title="E22">A8</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_1"/><i><font color="Green" title="E23">A9</font></i>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a2</font>
 ;<br/><a NAME="E2:15_1_1"/><i><font color="Green" title="E24">A10</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E3:15_1_1"/><i><font color="Green" title="E25">A11</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_1_1"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</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/>


</div><b>end;</b></div><a NAME="E4:15_1_1"/>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_1_2"/>
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_1_2_1"/><i><font color="Green" title="E26">A12</font></i>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font>
 ;<br/>

<a NAME="E2:15_1_1_2_1"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:15_1_1_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:15_1_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_1_2_1"><i><font color="Green" title="E26">A12</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:15_1_1_2"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_1"><i><font color="Green" title="E23">A9</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_1_2"/>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div><a NAME="E5:15_1_1"/><b>then </b>
<font color="Maroon" title="c16">b2'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">b3'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:15_1_1"><i><font color="Green" title="E24">A10</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_1"><i><font color="Green" title="E25">A11</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><a NAME="E6:15_1_1"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c17">b3'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_1"><i><font color="Green" title="E23">A9</font></i></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/><b>hence </b><a NAME="E7:15_1_1"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green" title="E23">A13</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_2"/><i><font color="Green" title="E24">A14</font></i>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font>
 ;<br/><a NAME="E2:15_1_2"/><i><font color="Green" title="E25">A15</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E3:15_1_2"/><i><font color="Green" title="E26">A16</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c15">b1'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_2_1"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c15">b1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:15_1_2"/>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c15">b1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_2"><i><font color="Green" title="E24">A14</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E5:15_1_2"/><b>then </b>
<font color="Maroon" title="c16">b2'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">b1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:15_1_2"><i><font color="Green" title="E25">A15</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_2"><i><font color="Green" title="E26">A16</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><b>hence </b><a NAME="E6:15_1_2"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_2"><i><font color="Green" title="E24">A14</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green" title="E24">A17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_3"/><i><font color="Green" title="E25">A18</font></i>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font>
 ;<br/><a NAME="E2:15_1_3"/><i><font color="Green" title="E26">A19</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_3_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</font>
 ;<br/>

<a NAME="E2:15_1_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:15_1_3"/><i><font color="Green" title="E27">A20</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c15">b1'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_3_2"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_3_2"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_3_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c15">b1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:15_1_3"/>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c15">b1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_3"><i><font color="Green" title="E25">A18</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><b>hence </b><a NAME="E5:15_1_3"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_3"><i><font color="Green" title="E25">A18</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_3"><i><font color="Green" title="E26">A19</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_3"><i><font color="Green" title="E27">A20</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4"/><i><font color="Green" title="E25">A21</font></i>: 
( <font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a3</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a3</font> )
 ;<br/><a NAME="E2:15_1_4"/><i><font color="Green" title="E26">A22</font></i>: 
( <font color="Maroon" title="c6">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c6">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_1"/><i><font color="Green" title="E27">A23</font></i>: 
( <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b2</font> or <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font> or <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font> )
 ;<br/>

<div><i><font color="Green" title="E28">A24</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_1_1"/><i><font color="Green" title="E29">A25</font></i>: 
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b2</font>
 ;<br/><a NAME="E2:15_1_4_1_1"/><i><font color="Green" title="E30">A26</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c13">a2'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c13">a2'</font>
 ;<br/>

<a NAME="E2:15_1_4_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:15_1_4_1_1"/><i><font color="Green" title="E31">A27</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c14">a3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_1_1_2"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c13">a2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_4_1_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c14">a3'</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/>


</div><b>end;</b></div><a NAME="E4:15_1_4_1_1"/>
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c13">a2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_1_1_3"/>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_1_1"><i><font color="Green" title="E29">A25</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_4_1_1_3"/>
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c13">a2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E5:15_1_4_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green" title="E25">A21</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_1_1"><i><font color="Green" title="E30">A26</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_1_1"><i><font color="Green" title="E31">A27</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E29">A28</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_1_2"/><i><font color="Green" title="E30">A29</font></i>: 
<font color="Maroon" title="c7">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font>
 ;<br/><a NAME="E2:15_1_4_1_2"/><i><font color="Green" title="E31">A30</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c12">a1'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c12">a1'</font>
 ;<br/>

<a NAME="E2:15_1_4_1_2_1"/><b>then </b><i><font color="Green" title="E32">A31</font></i>: 
<font color="Maroon" title="c12">a1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">N'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E3:15_1_4_1_2_1"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_1_4_1_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_1_2_1"><i><font color="Green" title="E32">A31</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:15_1_4_1_2"/><i><font color="Green" title="E32">A32</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_1_2_2"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c13">a2'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_4_1_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</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/>


</div><b>end;</b></div><a NAME="E4:15_1_4_1_2"/>
<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c13">a2'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_2_3"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_1_2_3"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_1_2"><i><font color="Green" title="E30">A29</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E2:15_1_4_1_2_3"/><b>then </b>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_1_2_3"/>
<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c13">a2'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E5:15_1_4_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green" title="E25">A21</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_1_2"><i><font color="Green" title="E31">A30</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_1_2"><i><font color="Green" title="E32">A32</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_1_3"/><i><font color="Green" title="E30">A33</font></i>: 
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font>
 ;<br/><a NAME="E2:15_1_4_1_3"/><i><font color="Green" title="E31">A34</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c12">a1'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_1_3_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c12">a1'</font>
 ;<br/>

<a NAME="E2:15_1_4_1_3_1"/><b>then </b><i><font color="Green" title="E32">A35</font></i>: 
<font color="Maroon" title="c12">a1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">N'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E3:15_1_4_1_3_1"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_1_4_1_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_1_3_1"><i><font color="Green" title="E32">A35</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:15_1_4_1_3"/><i><font color="Green" title="E32">A36</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_3_2"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_1_3_2"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_4_1_3_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</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/>


</div><b>end;</b></div><a NAME="E4:15_1_4_1_3"/>
<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c14">a3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_3_3"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_1_3_3"/>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_1_3"><i><font color="Green" title="E30">A33</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_4_1_3_3"/>
<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c14">a3'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E5:15_1_4_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green" title="E25">A21</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_1_3"><i><font color="Green" title="E31">A34</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_1_3"><i><font color="Green" title="E32">A36</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:15_1_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4_1"><i><font color="Green" title="E27">A23</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_1"><i><font color="Green" title="E28">A24</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_1"><i><font color="Green" title="E29">A28</font></i></a></i>;<br/>


</div><b>end;</b></div><div><i><font color="Green" title="E27">A37</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_2"/><i><font color="Green" title="E28">A38</font></i>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>
 ;<br/><b>consider </b><font color="Maroon" title="c20">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E3:15_1_4_2"/><i><font color="Green" title="E29">A39</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">x</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c21">x'</font> = <font color="Maroon" title="c20">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E5:15_1_4_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c21">x'</font>,<font color="Maroon" title="c21">x'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/><b>then consider </b><font color="Maroon" title="c22">A'</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E7:15_1_4_2"/><i><font color="Green" title="E30">A40</font></i>: 
( <font color="Maroon" title="c22">A'</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c11">o'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font> &amp; <font color="Maroon" title="c21">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font> &amp; <font color="Maroon" title="c21">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c23">A</font> = <font color="Maroon" title="c22">A'</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></i>;<br/><a NAME="E9:15_1_4_2"/><i><font color="Green" title="E31">A41</font></i>: 
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c10">N</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_2_1"/><i><font color="Green" title="E32">A42</font></i>: 
<font color="Maroon" title="c23">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_2_1_1"/><i><font color="Green" title="E33">A43</font></i>: 
for <font color="Olive" title="b1">e1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> holds <br/> <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Olive" title="b1">e1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c24">e1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>;<br/>

<b>assume </b><a NAME="E1:15_1_4_2_1_1_1"/><i><font color="Green" title="E34">A44</font></i>: 
<font color="Maroon" title="c24">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c25">e1'</font> = <font color="Maroon" title="c24">e1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E3:15_1_4_2_1_1_1"/>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E4:15_1_4_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c21">x'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">e1'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_1_1_1"><i><font color="Green" title="E34">A44</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E5:15_1_4_2_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c21">x'</font>,<font color="Maroon" title="c25">e1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:15_1_4_2_1_1_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c24">e1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:15_1_4_2_1_1"/>
for <font color="Olive" title="b1">e1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Olive" title="b1">e1</font> holds <br/><font color="Olive" title="b1">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c24">e1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>;<br/>

<b>assume </b><a NAME="E1:15_1_4_2_1_1_2"/><i><font color="Green" title="E34">A45</font></i>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c24">e1</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c25">e1'</font> = <font color="Maroon" title="c24">e1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E3:15_1_4_2_1_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c21">x'</font>,<font color="Maroon" title="c25">e1'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4_2_1_1_2"><i><font color="Green" title="E34">A45</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E4:15_1_4_2_1_1_2"/>
<font color="Maroon" title="c24">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_2"><i><font color="Green" title="E29">A39</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:15_1_4_2_1_1"/>
<font color="Maroon" title="c23">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4_2_1_1"><i><font color="Green" title="E33">A43</font></i></a>, <a class="ref" href="analmetr.html#D12" title="ANALMETR:def.12">ANALMETR:def 12</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:15_1_4_2_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c10">N</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_2"><i><font color="Green" title="E29">A39</font></i></a>, <a class="ref" href="analmetr.html#T77" title="ANALMETR:th.77">ANALMETR:77</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_2_1"/>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c10">N</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_2"><i><font color="Green" title="E29">A39</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_1"><i><font color="Green" title="E32">A42</font></i></a>, <a class="ref" href="analmetr.html#D15" title="ANALMETR:def.15">ANALMETR:def 15</a></i>;<br/>


</div><b>end;</b></div><b>consider </b><font color="Maroon" title="c24">e1'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E11:15_1_4_2"/><i><font color="Green" title="E32">A46</font></i>: 
( <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c24">e1'</font> &amp; <font color="Maroon" title="c17">b3'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">e1'</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E12:15_1_4_2"/>
not <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c24">e1'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_2"/><i><font color="Green" title="E33">A47</font></i>: 
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c24">e1'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c25">d1'</font>, <font color="Maroon" title="c26">d2'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E3:15_1_4_2_2"/><i><font color="Green" title="E34">A48</font></i>: 
( <font color="Maroon" title="c25">d1'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">d2'</font> &amp; <font color="Maroon" title="c22">A'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c25">d1'</font>,<font color="Maroon" title="c26">d2'</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="ref" href="aff_1.html#D3" title="AFF_1:def.3">AFF_1:def 3</a></i>;<br/>
<a NAME="E4:15_1_4_2_2"/><i><font color="Green" title="E35">A49</font></i>: 
( <font color="Maroon" title="c25">d1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font> &amp; <font color="Maroon" title="c26">d2'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_2_2"><i><font color="Green" title="E34">A48</font></i></a>, <a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a></i>;<br/>
<a NAME="E5:15_1_4_2_2"/>
<font color="Maroon" title="c25">d1'</font>,<font color="Maroon" title="c26">d2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1'</font>,<font color="Maroon" title="c26">d2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E6:15_1_4_2_2"/><b>then </b>
<font color="Maroon" title="c25">d1'</font>,<font color="Maroon" title="c26">d2'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_2_2"><i><font color="Green" title="E34">A48</font></i></a>, <a class="ref" href="aff_1.html#D4" title="AFF_1:def.4">AFF_1:def 4</a></i>;<br/>
<a NAME="E7:15_1_4_2_2"/><b>then </b><i><font color="Green" title="E36">A50</font></i>: 
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c24">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1'</font>,<font color="Maroon" title="c26">d2'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_2"><i><font color="Green" title="E33">A47</font></i></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c27">d1</font> = <font color="Maroon" title="c25">d1'</font>, <font color="Maroon" title="c28">d2</font> = <font color="Maroon" title="c26">d2'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E9:15_1_4_2_2"/>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1'</font>,<font color="Maroon" title="c26">d2'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E11:15_1_4_2"><i><font color="Green" title="E32">A46</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2_2"><i><font color="Green" title="E36">A50</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E10:15_1_4_2_2"/><b>then </b><i><font color="Green" title="E37">A51</font></i>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d1</font>,<font color="Maroon" title="c28">d2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E11:15_1_4_2_2"/>
<font color="Maroon" title="c27">d1</font>,<font color="Maroon" title="c28">d2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green" title="E31">A41</font></i></a>, <a class="txt" href="conmetr.html#E4:15_1_4_2_2"><i><font color="Green" title="E35">A49</font></i></a>, <a class="ref" href="analmetr.html#T78" title="ANALMETR:th.78">ANALMETR:78</a></i>;<br/>
<a NAME="E12:15_1_4_2_2"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_2_2"><i><font color="Green" title="E34">A48</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_2_2"><i><font color="Green" title="E37">A51</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E13:15_1_4_2_2"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2"><i><font color="Green" title="E28">A38</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E14:15_1_4_2_2"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E15:15_1_4_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E16:15_1_4_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E17:15_1_4_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green" title="E26">A22</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c25">c3'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E14:15_1_4_2"/><i><font color="Green" title="E33">A52</font></i>: 
( <font color="Maroon" title="c25">c3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c24">e1'</font>,<font color="Maroon" title="c25">c3'</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="ref" href="aff_1.html#T73" title="AFF_1:th.73">AFF_1:73</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c26">c3</font> = <font color="Maroon" title="c25">c3'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E16:15_1_4_2"/><i><font color="Green" title="E34">A53</font></i>: 
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c24">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c25">c3'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green" title="E33">A52</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E17:15_1_4_2"/><b>then </b><i><font color="Green" title="E35">A54</font></i>: 
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c25">c3'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E11:15_1_4_2"><i><font color="Green" title="E32">A46</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><b>consider </b><font color="Maroon" title="c27">e1'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E19:15_1_4_2"/><i><font color="Green" title="E36">A55</font></i>: 
( <font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c27">e1'</font> &amp; <font color="Maroon" title="c13">a2'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">e1'</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E20:15_1_4_2"/>
not <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c27">e1'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_3"/><i><font color="Green" title="E37">A56</font></i>: 
<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c27">e1'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 ;<br/>

<a NAME="E2:15_1_4_2_3"/>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E3:15_1_4_2_3"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green" title="E33">A52</font></i></a>, <a class="ref" href="aff_1.html#T54" title="AFF_1:th.54">AFF_1:54</a></i>;<br/>
<a NAME="E4:15_1_4_2_3"/><b>then </b>
<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c27">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_3"><i><font color="Green" title="E37">A56</font></i></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></i>;<br/>
<a NAME="E5:15_1_4_2_3"/><b>then </b>
<font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E19:15_1_4_2"><i><font color="Green" title="E36">A55</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E6:15_1_4_2_3"/><b>then </b>
<font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E7:15_1_4_2_3"/><b>then </b><i><font color="Green" title="E38">A57</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</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="E8:15_1_4_2_3"/>
<font color="Maroon" title="c25">c3'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">o'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_3_1"/>
<font color="Maroon" title="c25">c3'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">o'</font>
 ;<br/>

<a NAME="E2:15_1_4_2_3_1"/><b>then </b><i><font color="Green" title="E39">A58</font></i>: 
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E11:15_1_4_2"><i><font color="Green" title="E32">A46</font></i></a>, <a class="txt" href="conmetr.html#E16:15_1_4_2"><i><font color="Green" title="E34">A53</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:15_1_4_2_3_1"/>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_1_4_2_3_1"/><b>then </b>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_2_3_1"><i><font color="Green" title="E39">A58</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E5:15_1_4_2_3_1"/><b>then </b>
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E6:15_1_4_2_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:15_1_4_2_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green" title="E26">A22</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:15_1_4_2_3"/><b>then </b><i><font color="Green" title="E39">A59</font></i>: 
<font color="Maroon" title="c14">a3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green" title="E33">A52</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2_3"><i><font color="Green" title="E38">A57</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E10:15_1_4_2_3"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E11:15_1_4_2_3"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2_3"><i><font color="Green" title="E39">A59</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E12:15_1_4_2_3"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E13:15_1_4_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green" title="E31">A41</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c28">c2'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E22:15_1_4_2"/><i><font color="Green" title="E37">A60</font></i>: 
( <font color="Maroon" title="c28">c2'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c27">e1'</font>,<font color="Maroon" title="c28">c2'</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="ref" href="aff_1.html#T73" title="AFF_1:th.73">AFF_1:73</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c29">c2</font> = <font color="Maroon" title="c28">c2'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E24:15_1_4_2"/>
<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c27">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c28">c2'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E22:15_1_4_2"><i><font color="Green" title="E37">A60</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="E25:15_1_4_2"/><b>then </b>
<font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c28">c2'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E19:15_1_4_2"><i><font color="Green" title="E36">A55</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E26:15_1_4_2"/><b>then </b><i><font color="Green" title="E38">A61</font></i>: 
( <font color="Maroon" title="c29">c2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c29">c2</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E22:15_1_4_2"><i><font color="Green" title="E37">A60</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E27:15_1_4_2"/><b>then </b><i><font color="Green" title="E39">A62</font></i>: 
( <font color="Maroon" title="c29">c2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c26">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c29">c2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><b>consider </b><font color="Maroon" title="c30">e1'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E29:15_1_4_2"/><i><font color="Green" title="E40">A63</font></i>: 
( <font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c30">e1'</font> &amp; <font color="Maroon" title="c12">a1'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c30">e1'</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E30:15_1_4_2"/>
not <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c30">e1'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_4"/><i><font color="Green" title="E41">A64</font></i>: 
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c30">e1'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 ;<br/>

<a NAME="E2:15_1_4_2_4"/>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E3:15_1_4_2_4"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green" title="E33">A52</font></i></a>, <a class="ref" href="aff_1.html#T54" title="AFF_1:th.54">AFF_1:54</a></i>;<br/>
<a NAME="E4:15_1_4_2_4"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c30">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_4"><i><font color="Green" title="E41">A64</font></i></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></i>;<br/>
<a NAME="E5:15_1_4_2_4"/><b>then </b>
<font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E29:15_1_4_2"><i><font color="Green" title="E40">A63</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E6:15_1_4_2_4"/><b>then </b>
<font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E7:15_1_4_2_4"/><b>then </b><i><font color="Green" title="E42">A65</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</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="E8:15_1_4_2_4"/>
<font color="Maroon" title="c25">c3'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">o'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_4_1"/>
<font color="Maroon" title="c25">c3'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">o'</font>
 ;<br/>

<a NAME="E2:15_1_4_2_4_1"/><b>then </b><i><font color="Green" title="E43">A66</font></i>: 
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E11:15_1_4_2"><i><font color="Green" title="E32">A46</font></i></a>, <a class="txt" href="conmetr.html#E16:15_1_4_2"><i><font color="Green" title="E34">A53</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:15_1_4_2_4_1"/>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_1_4_2_4_1"/><b>then </b>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_2_4_1"><i><font color="Green" title="E43">A66</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E5:15_1_4_2_4_1"/><b>then </b>
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E6:15_1_4_2_4_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:15_1_4_2_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green" title="E26">A22</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:15_1_4_2_4"/><b>then </b><i><font color="Green" title="E43">A67</font></i>: 
<font color="Maroon" title="c14">a3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green" title="E33">A52</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2_4"><i><font color="Green" title="E42">A65</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E10:15_1_4_2_4"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E11:15_1_4_2_4"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2_4"><i><font color="Green" title="E43">A67</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E12:15_1_4_2_4"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E13:15_1_4_2_4"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green" title="E31">A41</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c31">c1'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E32:15_1_4_2"/><i><font color="Green" title="E41">A68</font></i>: 
( <font color="Maroon" title="c31">c1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c30">e1'</font>,<font color="Maroon" title="c31">c1'</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="ref" href="aff_1.html#T73" title="AFF_1:th.73">AFF_1:73</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c32">c1</font> = <font color="Maroon" title="c31">c1'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E34:15_1_4_2"/>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c30">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c31">c1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E32:15_1_4_2"><i><font color="Green" title="E41">A68</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="E35:15_1_4_2"/><b>then </b>
<font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c31">c1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E29:15_1_4_2"><i><font color="Green" title="E40">A63</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E36:15_1_4_2"/><b>then </b><i><font color="Green" title="E42">A69</font></i>: 
( <font color="Maroon" title="c32">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c32">c1</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E32:15_1_4_2"><i><font color="Green" title="E41">A68</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E37:15_1_4_2"/><b>then </b><i><font color="Green" title="E43">A70</font></i>: 
( <font color="Maroon" title="c32">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c26">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c32">c1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E38:15_1_4_2"/><i><font color="Green" title="E44">A71</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">c3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c29">c2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c32">c1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_5"/><i><font color="Green" title="E45">A72</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">c3</font> or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">c2</font> or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c32">c1</font> )
 ;<br/>

<div><i><font color="Green" title="E46">A73</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_5_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_2_5_1"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">c3</font>
 ;<br/><a NAME="E2:15_1_4_2_5_1"/><b>then </b><i><font color="Green" title="E47">A74</font></i>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c2">o</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E17:15_1_4_2"><i><font color="Green" title="E35">A54</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E3:15_1_4_2_5_1"/>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:15_1_4_2_5_1"/><b>then </b>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E5:15_1_4_2_5_1"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_2_5_1"><i><font color="Green" title="E47">A74</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/><a NAME="E6:15_1_4_2_5_1"/><b>then </b>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E7:15_1_4_2_5_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E8:15_1_4_2_5_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">a3'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><b>hence </b><a NAME="E9:15_1_4_2_5_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green" title="E26">A22</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_5_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_2_5_2"/>
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">c2</font> or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c32">c1</font> )
 ;<br/><a NAME="E2:15_1_4_2_5_2"/><b>then </b><i><font color="Green" title="E47">A75</font></i>: 
( <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c26">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c2">o</font> or <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c26">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E26:15_1_4_2"><i><font color="Green" title="E38">A61</font></i></a>, <a class="txt" href="conmetr.html#E36:15_1_4_2"><i><font color="Green" title="E42">A69</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E3:15_1_4_2_5_2"/>
( <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c14">a3'</font> &amp; <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c14">a3'</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:15_1_4_2_5_2"/><b>then </b>
( <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> &amp; <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E5:15_1_4_2_5_2"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c26">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_2_5_2"><i><font color="Green" title="E47">A75</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/><a NAME="E6:15_1_4_2_5_2"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c26">c3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E7:15_1_4_2_5_2"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c26">c3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E8:15_1_4_2_5_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c25">c3'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E9:15_1_4_2_5_2"/><b>then </b><i><font color="Green" title="E48">A76</font></i>: 
<font color="Maroon" title="c25">c3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green" title="E25">A21</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E10:15_1_4_2_5_2"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/><a NAME="E11:15_1_4_2_5_2"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green" title="E33">A52</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_2_5"><i><font color="Green" title="E46">A73</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2_5_2"><i><font color="Green" title="E48">A76</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/><a NAME="E12:15_1_4_2_5_2"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/><b>hence </b><a NAME="E13:15_1_4_2_5_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green" title="E31">A41</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:15_1_4_2_5"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4_2_5"><i><font color="Green" title="E45">A72</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_2_5"><i><font color="Green" title="E46">A73</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E39:15_1_4_2"/><i><font color="Green" title="E45">A77</font></i>: 
( not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_6"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font> or  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font> )
 ;<br/>

<a NAME="E2:15_1_4_2_6"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c14">a3'</font> or  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c14">a3'</font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_2_6"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green" title="E26">A22</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E40:15_1_4_2"/><i><font color="Green" title="E46">A78</font></i>: 
( not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c26">c3</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c26">c3</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_7"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c26">c3</font> or  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c26">c3</font> )
 ;<br/>

<a NAME="E2:15_1_4_2_7"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c25">c3'</font> or  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c25">c3'</font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:15_1_4_2_7"/><b>then </b><i><font color="Green" title="E47">A79</font></i>: 
( <font color="Maroon" title="c25">c3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M'</font> or <font color="Maroon" title="c25">c3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M'</font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green" title="E25">A21</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:15_1_4_2_7"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E5:15_1_4_2_7"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green" title="E33">A52</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_2"><i><font color="Green" title="E44">A71</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_2_7"><i><font color="Green" title="E47">A79</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E6:15_1_4_2_7"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E7:15_1_4_2_7"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green" title="E31">A41</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E41:15_1_4_2"/><i><font color="Green" title="E47">A80</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c6">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_8"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_2_8"/>
( <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font> &amp; <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font> &amp; <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c13">a2'</font> &amp; <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font> &amp; <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c13">a2'</font> &amp; <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E2:15_1_4_2_8"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c15">b1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c13">a2'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c15">b1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_2_8"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c6">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E42:15_1_4_2"/><i><font color="Green" title="E48">A81</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c32">c1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c29">c2</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c29">c2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_9"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_2_9"/>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E2:15_1_4_2_9"/><b>then </b>
( <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c31">c1'</font> &amp; <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c28">c2'</font> &amp; <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c31">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c28">c2'</font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green" title="E33">A52</font></i></a>, <a class="txt" href="conmetr.html#E22:15_1_4_2"><i><font color="Green" title="E37">A60</font></i></a>, <a class="txt" href="conmetr.html#E32:15_1_4_2"><i><font color="Green" title="E41">A68</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:15_1_4_2_9"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c31">c1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c28">c2'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c31">c1'</font>,<font color="Maroon" title="c28">c2'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:15_1_4_2_9"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c32">c1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c29">c2</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c29">c2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E43:15_1_4_2"/><b>then </b>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c26">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c32">c1</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:15"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_2"><i><font color="Green" title="E43">A70</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_2"><i><font color="Green" title="E44">A71</font></i></a>, <a class="txt" href="conmetr.html#E39:15_1_4_2"><i><font color="Green" title="E45">A77</font></i></a>, <a class="txt" href="conmetr.html#E40:15_1_4_2"><i><font color="Green" title="E46">A78</font></i></a>, <a class="txt" href="conmetr.html#E41:15_1_4_2"><i><font color="Green" title="E47">A80</font></i></a>, <a class="ref" href="conaffm.html#D1" title="CONAFFM:def.1">CONAFFM:def 1</a></i>;<br/><a NAME="E44:15_1_4_2"/><b>then </b><i><font color="Green" title="E49">A82</font></i>: 
<font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c6">b1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E45:15_1_4_2"/>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c26">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c29">c2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:15"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E27:15_1_4_2"><i><font color="Green" title="E39">A62</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_2"><i><font color="Green" title="E44">A71</font></i></a>, <a class="txt" href="conmetr.html#E39:15_1_4_2"><i><font color="Green" title="E45">A77</font></i></a>, <a class="txt" href="conmetr.html#E40:15_1_4_2"><i><font color="Green" title="E46">A78</font></i></a>, <a class="txt" href="conmetr.html#E41:15_1_4_2"><i><font color="Green" title="E47">A80</font></i></a>, <a class="txt" href="conmetr.html#E42:15_1_4_2"><i><font color="Green" title="E48">A81</font></i></a>, <a class="ref" href="conaffm.html#D1" title="CONAFFM:def.1">CONAFFM:def 1</a></i>;<br/><a NAME="E46:15_1_4_2"/><b>then </b><i><font color="Green" title="E50">A83</font></i>: 
<font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">c2</font>,<font color="Maroon" title="c6">b1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E47:15_1_4_2"/><i><font color="Green" title="E51">A84</font></i>: 
not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_10"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_10"/><i><font color="Green" title="E52">A85</font></i>: 
<font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 ;<br/>

<a NAME="E2:15_1_4_2_10"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E3:15_1_4_2_10"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c19">N'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_10"><i><font color="Green" title="E52">A85</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E4:15_1_4_2_10"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c10">N</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_2_10"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green" title="E31">A41</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E48:15_1_4_2"/>
not <font color="Maroon" title="c26">c3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_11"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_11"/><i><font color="Green" title="E52">A86</font></i>: 
<font color="Maroon" title="c26">c3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 ;<br/>

<a NAME="E2:15_1_4_2_11"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E3:15_1_4_2_11"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c19">N'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green" title="E33">A52</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_2"><i><font color="Green" title="E44">A71</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_11"><i><font color="Green" title="E52">A86</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E4:15_1_4_2_11"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c10">N</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_2_11"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green" title="E31">A41</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E49:15_1_4_2"/><b>then </b><i><font color="Green" title="E52">A87</font></i>: 
<font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">c2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green" title="E31">A41</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green" title="E33">A52</font></i></a>, <a class="txt" href="conmetr.html#E22:15_1_4_2"><i><font color="Green" title="E37">A60</font></i></a>, <a class="txt" href="conmetr.html#E32:15_1_4_2"><i><font color="Green" title="E41">A68</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_2"><i><font color="Green" title="E44">A71</font></i></a>, <a class="txt" href="conmetr.html#E44:15_1_4_2"><i><font color="Green" title="E49">A82</font></i></a>, <a class="txt" href="conmetr.html#E46:15_1_4_2"><i><font color="Green" title="E50">A83</font></i></a>, <a class="txt" href="conmetr.html#E47:15_1_4_2"><i><font color="Green" title="E51">A84</font></i></a>, <a class="ref" href="conmetr.html#D1" target="_self" title="CONMETR:def.1">Def1</a></i>;<br/><a NAME="E50:15_1_4_2"/><i><font color="Green" title="E53">A88</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c32">c1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_12"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_12"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c32">c1</font>
 ;<br/>

<a NAME="E2:15_1_4_2_12"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c31">c1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:15_1_4_2_12"/><b>then </b><i><font color="Green" title="E54">A89</font></i>: 
<font color="Maroon" title="c31">c1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green" title="E25">A21</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:15_1_4_2_12"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c31">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c31">c1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E5:15_1_4_2_12"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E32:15_1_4_2"><i><font color="Green" title="E41">A68</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_2"><i><font color="Green" title="E44">A71</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_2_12"><i><font color="Green" title="E54">A89</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E6:15_1_4_2_12"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E7:15_1_4_2_12"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green" title="E31">A41</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E51:15_1_4_2"/><i><font color="Green" title="E54">A90</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c29">c2</font>,<font color="Maroon" title="c7">b2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_13"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_13"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c29">c2</font>,<font color="Maroon" title="c7">b2</font>
 ;<br/>

<a NAME="E2:15_1_4_2_13"/><b>then </b><i><font color="Green" title="E55">A91</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c31">c1'</font>,<font color="Maroon" title="c28">c2'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:15_1_4_2_13"/>
<font color="Maroon" title="c31">c1'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">c2'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_13_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_13_1"/><i><font color="Green" title="E56">A92</font></i>: 
<font color="Maroon" title="c31">c1'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">c2'</font>
 ;<br/>

<a NAME="E2:15_1_4_2_13_1"/>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">c3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_13_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_13_1_1"/><i><font color="Green" title="E57">A93</font></i>: 
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">c3</font>
 ;<br/>

<a NAME="E2:15_1_4_2_13_1_1"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E3:15_1_4_2_13_1_1"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green" title="E33">A52</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_13_1_1"><i><font color="Green" title="E57">A93</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E4:15_1_4_2_13_1_1"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_2_13_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green" title="E31">A41</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:15_1_4_2_13_1"/><b>then </b>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c32">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c32">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E27:15_1_4_2"><i><font color="Green" title="E39">A62</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_2"><i><font color="Green" title="E43">A70</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_13_1"><i><font color="Green" title="E56">A92</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:15_1_4_2_13_1"/><b>then </b>
<font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c4">a2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:15_1_4_2_13_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:15_1_4_2_13_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c31">c1'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:15_1_4_2_13_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c31">c1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E8:15_1_4_2_13_1"/><b>then </b><i><font color="Green" title="E57">A94</font></i>: 
<font color="Maroon" title="c31">c1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green" title="E25">A21</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E9:15_1_4_2_13_1"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c31">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c31">c1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E10:15_1_4_2_13_1"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E32:15_1_4_2"><i><font color="Green" title="E41">A68</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_2"><i><font color="Green" title="E44">A71</font></i></a>, <a class="txt" href="conmetr.html#E8:15_1_4_2_13_1"><i><font color="Green" title="E57">A94</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E11:15_1_4_2_13_1"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E12:15_1_4_2_13_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green" title="E31">A41</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:15_1_4_2_13"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E22:15_1_4_2"><i><font color="Green" title="E37">A60</font></i></a>, <a class="txt" href="conmetr.html#E32:15_1_4_2"><i><font color="Green" title="E41">A68</font></i></a>, <a class="txt" href="conmetr.html#E47:15_1_4_2"><i><font color="Green" title="E51">A84</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_2_13"><i><font color="Green" title="E55">A91</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E52:15_1_4_2"/>
<font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">c2</font>,<font color="Maroon" title="c4">a2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_14"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_2_14"/>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">c3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_14_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_14_1"/><i><font color="Green" title="E55">A95</font></i>: 
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">c3</font>
 ;<br/>

<a NAME="E2:15_1_4_2_14_1"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E3:15_1_4_2_14_1"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green" title="E30">A40</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green" title="E33">A52</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_14_1"><i><font color="Green" title="E55">A95</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E4:15_1_4_2_14_1"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_2_14_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green" title="E31">A41</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:15_1_4_2_14"/><b>then </b>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c29">c2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c32">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E27:15_1_4_2"><i><font color="Green" title="E39">A62</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_2"><i><font color="Green" title="E43">A70</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_2_14"/>
<font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">c2</font>,<font color="Maroon" title="c4">a2</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E53:15_1_4_2"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:15"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_2"><i><font color="Green" title="E44">A71</font></i></a>, <a class="txt" href="conmetr.html#E41:15_1_4_2"><i><font color="Green" title="E47">A80</font></i></a>, <a class="txt" href="conmetr.html#E42:15_1_4_2"><i><font color="Green" title="E48">A81</font></i></a>, <a class="txt" href="conmetr.html#E49:15_1_4_2"><i><font color="Green" title="E52">A87</font></i></a>, <a class="txt" href="conmetr.html#E50:15_1_4_2"><i><font color="Green" title="E53">A88</font></i></a>, <a class="txt" href="conmetr.html#E51:15_1_4_2"><i><font color="Green" title="E54">A90</font></i></a>, <a class="ref" href="conaffm.html#D1" title="CONAFFM:def.1">CONAFFM:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_3"/><i><font color="Green" title="E28">A96</font></i>: 
not <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>
 ;<br/><b>consider </b><font color="Maroon" title="c20">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E3:15_1_4_3"/><i><font color="Green" title="E29">A97</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">x</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c21">x'</font> = <font color="Maroon" title="c20">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E5:15_1_4_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c21">x'</font>,<font color="Maroon" title="c21">x'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/><b>then consider </b><font color="Maroon" title="c22">A'</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E7:15_1_4_3"/><i><font color="Green" title="E30">A98</font></i>: 
( <font color="Maroon" title="c22">A'</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c11">o'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font> &amp; <font color="Maroon" title="c21">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font> &amp; <font color="Maroon" title="c21">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c23">A</font> = <font color="Maroon" title="c22">A'</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></i>;<br/><a NAME="E9:15_1_4_3"/><i><font color="Green" title="E31">A99</font></i>: 
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c22">A'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E10:15_1_4_3"/><i><font color="Green" title="E32">A100</font></i>: 
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c10">N</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_1"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_3_1"/><i><font color="Green" title="E33">A101</font></i>: 
<font color="Maroon" title="c23">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_3_1_1"/><i><font color="Green" title="E34">A102</font></i>: 
for <font color="Olive" title="b1">e1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> holds <br/> <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Olive" title="b1">e1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c24">e1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>;<br/>

<b>assume </b><a NAME="E1:15_1_4_3_1_1_1"/><i><font color="Green" title="E35">A103</font></i>: 
<font color="Maroon" title="c24">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c25">e1'</font> = <font color="Maroon" title="c24">e1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E3:15_1_4_3_1_1_1"/>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E4:15_1_4_3_1_1_1"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c21">x'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">e1'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_1_1_1"><i><font color="Green" title="E35">A103</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E5:15_1_4_3_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c21">x'</font>,<font color="Maroon" title="c25">e1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:15_1_4_3_1_1_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c24">e1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:15_1_4_3_1_1"/>
for <font color="Olive" title="b1">e1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Olive" title="b1">e1</font> holds <br/><font color="Olive" title="b1">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c24">e1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>;<br/>

<b>assume </b><a NAME="E1:15_1_4_3_1_1_2"/><i><font color="Green" title="E35">A104</font></i>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c24">e1</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c25">e1'</font> = <font color="Maroon" title="c24">e1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E3:15_1_4_3_1_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c21">x'</font>,<font color="Maroon" title="c25">e1'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4_3_1_1_2"><i><font color="Green" title="E35">A104</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E4:15_1_4_3_1_1_2"/>
<font color="Maroon" title="c24">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_3"><i><font color="Green" title="E29">A97</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:15_1_4_3_1_1"/>
<font color="Maroon" title="c23">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4_3_1_1"><i><font color="Green" title="E34">A102</font></i></a>, <a class="ref" href="analmetr.html#D12" title="ANALMETR:def.12">ANALMETR:def 12</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:15_1_4_3_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c10">N</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_3"><i><font color="Green" title="E29">A97</font></i></a>, <a class="ref" href="analmetr.html#T77" title="ANALMETR:th.77">ANALMETR:77</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_3_1"/>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c10">N</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_3"><i><font color="Green" title="E29">A97</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_1"><i><font color="Green" title="E33">A101</font></i></a>, <a class="ref" href="analmetr.html#D15" title="ANALMETR:def.15">ANALMETR:def 15</a></i>;<br/>


</div><b>end;</b></div><b>consider </b><font color="Maroon" title="c24">e1'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E12:15_1_4_3"/><i><font color="Green" title="E33">A105</font></i>: 
( <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c24">e1'</font> &amp; <font color="Maroon" title="c16">b2'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">e1'</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E13:15_1_4_3"/>
not <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c24">e1'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_2"/><i><font color="Green" title="E34">A106</font></i>: 
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c24">e1'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c25">d1'</font>, <font color="Maroon" title="c26">d2'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E3:15_1_4_3_2"/><i><font color="Green" title="E35">A107</font></i>: 
( <font color="Maroon" title="c25">d1'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">d2'</font> &amp; <font color="Maroon" title="c22">A'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c25">d1'</font>,<font color="Maroon" title="c26">d2'</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="ref" href="aff_1.html#D3" title="AFF_1:def.3">AFF_1:def 3</a></i>;<br/>
<a NAME="E4:15_1_4_3_2"/><i><font color="Green" title="E36">A108</font></i>: 
( <font color="Maroon" title="c25">d1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font> &amp; <font color="Maroon" title="c26">d2'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_3_2"><i><font color="Green" title="E35">A107</font></i></a>, <a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a></i>;<br/>
<a NAME="E5:15_1_4_3_2"/>
<font color="Maroon" title="c25">d1'</font>,<font color="Maroon" title="c26">d2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1'</font>,<font color="Maroon" title="c26">d2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E6:15_1_4_3_2"/><b>then </b>
<font color="Maroon" title="c25">d1'</font>,<font color="Maroon" title="c26">d2'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_3_2"><i><font color="Green" title="E35">A107</font></i></a>, <a class="ref" href="aff_1.html#D4" title="AFF_1:def.4">AFF_1:def 4</a></i>;<br/>
<a NAME="E7:15_1_4_3_2"/><b>then </b><i><font color="Green" title="E37">A109</font></i>: 
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c24">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1'</font>,<font color="Maroon" title="c26">d2'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_2"><i><font color="Green" title="E34">A106</font></i></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c27">d1</font> = <font color="Maroon" title="c25">d1'</font>, <font color="Maroon" title="c28">d2</font> = <font color="Maroon" title="c26">d2'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E9:15_1_4_3_2"/>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1'</font>,<font color="Maroon" title="c26">d2'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E12:15_1_4_3"><i><font color="Green" title="E33">A105</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3_2"><i><font color="Green" title="E37">A109</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E10:15_1_4_3_2"/><b>then </b><i><font color="Green" title="E38">A110</font></i>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d1</font>,<font color="Maroon" title="c28">d2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E11:15_1_4_3_2"/>
<font color="Maroon" title="c27">d1</font>,<font color="Maroon" title="c28">d2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green" title="E32">A100</font></i></a>, <a class="txt" href="conmetr.html#E4:15_1_4_3_2"><i><font color="Green" title="E36">A108</font></i></a>, <a class="ref" href="analmetr.html#T78" title="ANALMETR:th.78">ANALMETR:78</a></i>;<br/>
<b>hence </b><a NAME="E12:15_1_4_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4_3"><i><font color="Green" title="E28">A96</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_3_2"><i><font color="Green" title="E35">A107</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3_2"><i><font color="Green" title="E38">A110</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c25">c3'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E15:15_1_4_3"/><i><font color="Green" title="E34">A111</font></i>: 
( <font color="Maroon" title="c25">c3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c24">e1'</font>,<font color="Maroon" title="c25">c3'</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="ref" href="aff_1.html#T73" title="AFF_1:th.73">AFF_1:73</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c26">c3</font> = <font color="Maroon" title="c25">c3'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E17:15_1_4_3"/>
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c24">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c25">c3'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green" title="E34">A111</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="E18:15_1_4_3"/><b>then </b><i><font color="Green" title="E35">A112</font></i>: 
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c25">c3'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E12:15_1_4_3"><i><font color="Green" title="E33">A105</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><b>consider </b><font color="Maroon" title="c27">e1'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E20:15_1_4_3"/><i><font color="Green" title="E36">A113</font></i>: 
( <font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c27">e1'</font> &amp; <font color="Maroon" title="c12">a1'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">e1'</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E21:15_1_4_3"/>
not <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c27">e1'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_3"/><i><font color="Green" title="E37">A114</font></i>: 
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c27">e1'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 ;<br/>

<a NAME="E2:15_1_4_3_3"/>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E3:15_1_4_3_3"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green" title="E34">A111</font></i></a>, <a class="ref" href="aff_1.html#T54" title="AFF_1:th.54">AFF_1:54</a></i>;<br/>
<a NAME="E4:15_1_4_3_3"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c27">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_3"><i><font color="Green" title="E37">A114</font></i></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></i>;<br/>
<a NAME="E5:15_1_4_3_3"/><b>then </b>
<font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E20:15_1_4_3"><i><font color="Green" title="E36">A113</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E6:15_1_4_3_3"/><b>then </b>
<font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E7:15_1_4_3_3"/><b>then </b><i><font color="Green" title="E38">A115</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</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="E8:15_1_4_3_3"/>
<font color="Maroon" title="c25">c3'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">o'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_3_1"/>
<font color="Maroon" title="c25">c3'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">o'</font>
 ;<br/>

<a NAME="E2:15_1_4_3_3_1"/><b>then </b><i><font color="Green" title="E39">A116</font></i>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c2">o</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E18:15_1_4_3"><i><font color="Green" title="E35">A112</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:15_1_4_3_3_1"/>
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_1_4_3_3_1"/><b>then </b>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:15_1_4_3_3_1"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_3_3_1"><i><font color="Green" title="E39">A116</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E6:15_1_4_3_3_1"/><b>then </b>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E7:15_1_4_3_3_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E8:15_1_4_3_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E9:15_1_4_3_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green" title="E26">A22</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:15_1_4_3_3"/><b>then </b><i><font color="Green" title="E39">A117</font></i>: 
<font color="Maroon" title="c14">a3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green" title="E34">A111</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3_3"><i><font color="Green" title="E38">A115</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E10:15_1_4_3_3"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E11:15_1_4_3_3"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_3_3"><i><font color="Green" title="E39">A117</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E12:15_1_4_3_3"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E13:15_1_4_3_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green" title="E32">A100</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c28">c1'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E23:15_1_4_3"/><i><font color="Green" title="E37">A118</font></i>: 
( <font color="Maroon" title="c28">c1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c27">e1'</font>,<font color="Maroon" title="c28">c1'</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="ref" href="aff_1.html#T73" title="AFF_1:th.73">AFF_1:73</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c29">c1</font> = <font color="Maroon" title="c28">c1'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E25:15_1_4_3"/>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c27">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c28">c1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E23:15_1_4_3"><i><font color="Green" title="E37">A118</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="E26:15_1_4_3"/><b>then </b><i><font color="Green" title="E38">A119</font></i>: 
<font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c28">c1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E20:15_1_4_3"><i><font color="Green" title="E36">A113</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E27:15_1_4_3"/><b>then </b><i><font color="Green" title="E39">A120</font></i>: 
( <font color="Maroon" title="c29">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c29">c1</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E23:15_1_4_3"><i><font color="Green" title="E37">A118</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><b>consider </b><font color="Maroon" title="c30">e1'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E29:15_1_4_3"/><i><font color="Green" title="E40">A121</font></i>: 
( <font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c30">e1'</font> &amp; <font color="Maroon" title="c13">a2'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c30">e1'</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E30:15_1_4_3"/>
not <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c30">e1'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_4"/><i><font color="Green" title="E41">A122</font></i>: 
<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c30">e1'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 ;<br/>

<a NAME="E2:15_1_4_3_4"/>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E3:15_1_4_3_4"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green" title="E34">A111</font></i></a>, <a class="ref" href="aff_1.html#T54" title="AFF_1:th.54">AFF_1:54</a></i>;<br/>
<a NAME="E4:15_1_4_3_4"/><b>then </b>
<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c30">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_4"><i><font color="Green" title="E41">A122</font></i></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></i>;<br/>
<a NAME="E5:15_1_4_3_4"/><b>then </b>
<font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E29:15_1_4_3"><i><font color="Green" title="E40">A121</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E6:15_1_4_3_4"/><b>then </b>
<font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E7:15_1_4_3_4"/><b>then </b><i><font color="Green" title="E42">A123</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</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="E8:15_1_4_3_4"/>
<font color="Maroon" title="c25">c3'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">o'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_4_1"/>
<font color="Maroon" title="c25">c3'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">o'</font>
 ;<br/>

<a NAME="E2:15_1_4_3_4_1"/><b>then </b><i><font color="Green" title="E43">A124</font></i>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c2">o</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E18:15_1_4_3"><i><font color="Green" title="E35">A112</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:15_1_4_3_4_1"/>
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_1_4_3_4_1"/><b>then </b>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:15_1_4_3_4_1"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_3_4_1"><i><font color="Green" title="E43">A124</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E6:15_1_4_3_4_1"/><b>then </b>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E7:15_1_4_3_4_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E8:15_1_4_3_4_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E9:15_1_4_3_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green" title="E26">A22</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:15_1_4_3_4"/><b>then </b><i><font color="Green" title="E43">A125</font></i>: 
<font color="Maroon" title="c14">a3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green" title="E34">A111</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3_4"><i><font color="Green" title="E42">A123</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E10:15_1_4_3_4"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E11:15_1_4_3_4"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_3_4"><i><font color="Green" title="E43">A125</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E12:15_1_4_3_4"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E13:15_1_4_3_4"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green" title="E32">A100</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c31">c2'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E32:15_1_4_3"/><i><font color="Green" title="E41">A126</font></i>: 
( <font color="Maroon" title="c31">c2'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c30">e1'</font>,<font color="Maroon" title="c31">c2'</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="ref" href="aff_1.html#T73" title="AFF_1:th.73">AFF_1:73</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c32">c2</font> = <font color="Maroon" title="c31">c2'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E34:15_1_4_3"/>
<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c30">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c31">c2'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E32:15_1_4_3"><i><font color="Green" title="E41">A126</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="E35:15_1_4_3"/><b>then </b><i><font color="Green" title="E42">A127</font></i>: 
<font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c31">c2'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E29:15_1_4_3"><i><font color="Green" title="E40">A121</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E36:15_1_4_3"/><b>then </b><i><font color="Green" title="E43">A128</font></i>: 
( <font color="Maroon" title="c32">c2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c32">c2</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E32:15_1_4_3"><i><font color="Green" title="E41">A126</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E37:15_1_4_3"/><i><font color="Green" title="E44">A129</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">c3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c32">c2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c29">c1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_5"/><i><font color="Green" title="E45">A130</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">c3</font> or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c32">c2</font> or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">c1</font> )
 ;<br/>

<div><i><font color="Green" title="E46">A131</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_5_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_3_5_1"/><i><font color="Green" title="E47">A132</font></i>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">c3</font>
 ;<br/><a NAME="E2:15_1_4_3_5_1"/>
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E3:15_1_4_3_5_1"/><b>then </b>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E18:15_1_4_3"><i><font color="Green" title="E35">A112</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_5_1"><i><font color="Green" title="E47">A132</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E4:15_1_4_3_5_1"/><b>then </b>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">a3'</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="E5:15_1_4_3_5_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><b>hence </b><a NAME="E6:15_1_4_3_5_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green" title="E26">A22</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_5_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_3_5_2"/>
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c32">c2</font> or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">c1</font> )
 ;<br/><a NAME="E2:15_1_4_3_5_2"/><b>then </b><i><font color="Green" title="E47">A133</font></i>: 
( <font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font> or <font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c2">o</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E26:15_1_4_3"><i><font color="Green" title="E38">A119</font></i></a>, <a class="txt" href="conmetr.html#E35:15_1_4_3"><i><font color="Green" title="E42">A127</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E3:15_1_4_3_5_2"/>
( <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font> &amp; <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_5_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_3_5_2_1"/>
( <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font> &amp; <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_4_3_5_2_1"/>
( <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font> &amp; <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:15_1_4_3_5_2"/><b>then </b>
<font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_3_5_2"><i><font color="Green" title="E47">A133</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/><a NAME="E5:15_1_4_3_5_2"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c26">c3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E6:15_1_4_3_5_2"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c26">c3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E7:15_1_4_3_5_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c25">c3'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E8:15_1_4_3_5_2"/><b>then </b><i><font color="Green" title="E48">A134</font></i>: 
<font color="Maroon" title="c25">c3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green" title="E25">A21</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E9:15_1_4_3_5_2"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/><a NAME="E10:15_1_4_3_5_2"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green" title="E34">A111</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_3_5"><i><font color="Green" title="E46">A131</font></i></a>, <a class="txt" href="conmetr.html#E8:15_1_4_3_5_2"><i><font color="Green" title="E48">A134</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/><a NAME="E11:15_1_4_3_5_2"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/><b>hence </b><a NAME="E12:15_1_4_3_5_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green" title="E32">A100</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:15_1_4_3_5"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4_3_5"><i><font color="Green" title="E45">A130</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_3_5"><i><font color="Green" title="E46">A131</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E38:15_1_4_3"/><i><font color="Green" title="E45">A135</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c26">c3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_6"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c26">c3</font>
 ;<br/>

<a NAME="E2:15_1_4_3_6"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:15_1_4_3_6"/><b>then </b><i><font color="Green" title="E46">A136</font></i>: 
<font color="Maroon" title="c25">c3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green" title="E25">A21</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:15_1_4_3_6"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E5:15_1_4_3_6"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green" title="E34">A111</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green" title="E44">A129</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_3_6"><i><font color="Green" title="E46">A136</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E6:15_1_4_3_6"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E7:15_1_4_3_6"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green" title="E32">A100</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E39:15_1_4_3"/><i><font color="Green" title="E46">A137</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_7"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font>
 ;<br/>

<a NAME="E2:15_1_4_3_7"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_3_7"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green" title="E26">A22</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E40:15_1_4_3"/><i><font color="Green" title="E47">A138</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c6">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_8"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_3_8"/>
( <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font> &amp; <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font> &amp; <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c13">a2'</font> &amp; <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font> &amp; <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c13">a2'</font> &amp; <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E2:15_1_4_3_8"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c15">b1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c13">a2'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c15">b1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_3_8"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c6">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E41:15_1_4_3"/><i><font color="Green" title="E48">A139</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c29">c1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c32">c2</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c29">c1</font>,<font color="Maroon" title="c32">c2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_9"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_3_9"/>
( <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c28">c1'</font> &amp; <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c31">c2'</font> &amp; <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c28">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c31">c2'</font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_3"><i><font color="Green" title="E31">A99</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green" title="E34">A111</font></i></a>, <a class="txt" href="conmetr.html#E23:15_1_4_3"><i><font color="Green" title="E37">A118</font></i></a>, <a class="txt" href="conmetr.html#E32:15_1_4_3"><i><font color="Green" title="E41">A126</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E2:15_1_4_3_9"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c28">c1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>,<font color="Maroon" title="c31">c2'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c28">c1'</font>,<font color="Maroon" title="c31">c2'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_3_9"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c29">c1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c32">c2</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c29">c1</font>,<font color="Maroon" title="c32">c2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E42:15_1_4_3"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c26">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c29">c1</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E27:15_1_4_3"><i><font color="Green" title="E39">A120</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E43:15_1_4_3"/><b>then </b>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c26">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c29">c1</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:15"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green" title="E44">A129</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_3"><i><font color="Green" title="E45">A135</font></i></a>, <a class="txt" href="conmetr.html#E39:15_1_4_3"><i><font color="Green" title="E46">A137</font></i></a>, <a class="txt" href="conmetr.html#E40:15_1_4_3"><i><font color="Green" title="E47">A138</font></i></a>, <a class="txt" href="conmetr.html#E41:15_1_4_3"><i><font color="Green" title="E48">A139</font></i></a>, <a class="ref" href="conaffm.html#D1" title="CONAFFM:def.1">CONAFFM:def 1</a></i>;<br/><a NAME="E44:15_1_4_3"/><b>then </b><i><font color="Green" title="E49">A140</font></i>: 
<font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">c1</font>,<font color="Maroon" title="c6">b1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E45:15_1_4_3"/><i><font color="Green" title="E50">A141</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_10"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_10"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font>
 ;<br/>

<a NAME="E2:15_1_4_3_10"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_3_10"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green" title="E26">A22</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E46:15_1_4_3"/><i><font color="Green" title="E51">A142</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c26">c3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_11"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_11"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c26">c3</font>
 ;<br/>

<a NAME="E2:15_1_4_3_11"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:15_1_4_3_11"/><b>then </b><i><font color="Green" title="E52">A143</font></i>: 
<font color="Maroon" title="c25">c3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green" title="E25">A21</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:15_1_4_3_11"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E5:15_1_4_3_11"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green" title="E34">A111</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green" title="E44">A129</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_3_11"><i><font color="Green" title="E52">A143</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E6:15_1_4_3_11"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E7:15_1_4_3_11"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green" title="E32">A100</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E47:15_1_4_3"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c26">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c32">c2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E36:15_1_4_3"><i><font color="Green" title="E43">A128</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E48:15_1_4_3"/><b>then </b>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c26">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c32">c2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:15"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green" title="E44">A129</font></i></a>, <a class="txt" href="conmetr.html#E40:15_1_4_3"><i><font color="Green" title="E47">A138</font></i></a>, <a class="txt" href="conmetr.html#E41:15_1_4_3"><i><font color="Green" title="E48">A139</font></i></a>, <a class="txt" href="conmetr.html#E45:15_1_4_3"><i><font color="Green" title="E50">A141</font></i></a>, <a class="txt" href="conmetr.html#E46:15_1_4_3"><i><font color="Green" title="E51">A142</font></i></a>, <a class="ref" href="conaffm.html#D1" title="CONAFFM:def.1">CONAFFM:def 1</a></i>;<br/><a NAME="E49:15_1_4_3"/><b>then </b><i><font color="Green" title="E52">A144</font></i>: 
<font color="Maroon" title="c26">c3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">c2</font>,<font color="Maroon" title="c6">b1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E50:15_1_4_3"/><i><font color="Green" title="E53">A145</font></i>: 
not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_12"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_12"/><i><font color="Green" title="E54">A146</font></i>: 
<font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 ;<br/>

<a NAME="E2:15_1_4_3_12"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E3:15_1_4_3_12"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c19">N'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_12"><i><font color="Green" title="E54">A146</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E4:15_1_4_3_12"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c10">N</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_3_12"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green" title="E32">A100</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E51:15_1_4_3"/>
not <font color="Maroon" title="c26">c3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_13"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_13"/><i><font color="Green" title="E54">A147</font></i>: 
<font color="Maroon" title="c26">c3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 ;<br/>

<a NAME="E2:15_1_4_3_13"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E3:15_1_4_3_13"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c19">N'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green" title="E34">A111</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green" title="E44">A129</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_13"><i><font color="Green" title="E54">A147</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E4:15_1_4_3_13"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c10">N</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_3_13"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green" title="E32">A100</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E52:15_1_4_3"/><b>then </b><i><font color="Green" title="E54">A148</font></i>: 
<font color="Maroon" title="c29">c1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">c2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green" title="E32">A100</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green" title="E34">A111</font></i></a>, <a class="txt" href="conmetr.html#E23:15_1_4_3"><i><font color="Green" title="E37">A118</font></i></a>, <a class="txt" href="conmetr.html#E32:15_1_4_3"><i><font color="Green" title="E41">A126</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green" title="E44">A129</font></i></a>, <a class="txt" href="conmetr.html#E44:15_1_4_3"><i><font color="Green" title="E49">A140</font></i></a>, <a class="txt" href="conmetr.html#E49:15_1_4_3"><i><font color="Green" title="E52">A144</font></i></a>, <a class="txt" href="conmetr.html#E50:15_1_4_3"><i><font color="Green" title="E53">A145</font></i></a>, <a class="ref" href="conmetr.html#D1" target="_self" title="CONMETR:def.1">Def1</a></i>;<br/><a NAME="E53:15_1_4_3"/><i><font color="Green" title="E55">A149</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c29">c1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_14"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_14"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c29">c1</font>
 ;<br/>

<a NAME="E2:15_1_4_3_14"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c28">c1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:15_1_4_3_14"/><b>then </b><i><font color="Green" title="E56">A150</font></i>: 
<font color="Maroon" title="c28">c1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green" title="E25">A21</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:15_1_4_3_14"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c28">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c28">c1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E5:15_1_4_3_14"/><b>then </b>
<font color="Maroon" title="c18">M'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E23:15_1_4_3"><i><font color="Green" title="E37">A118</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green" title="E44">A129</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_3_14"><i><font color="Green" title="E56">A150</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E6:15_1_4_3_14"/><b>then </b>
<font color="Maroon" title="c9">M</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c23">A</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E7:15_1_4_3_14"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green" title="E32">A100</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E54:15_1_4_3"/><i><font color="Green" title="E56">A151</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c29">c1</font>,<font color="Maroon" title="c32">c2</font>,<font color="Maroon" title="c7">b2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_15"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_15"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c29">c1</font>,<font color="Maroon" title="c32">c2</font>,<font color="Maroon" title="c7">b2</font>
 ;<br/>

<a NAME="E2:15_1_4_3_15"/><b>then </b><i><font color="Green" title="E57">A152</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c28">c1'</font>,<font color="Maroon" title="c31">c2'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:15_1_4_3_15"/>
<font color="Maroon" title="c28">c1'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c31">c2'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_15_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_15_1"/><i><font color="Green" title="E58">A153</font></i>: 
<font color="Maroon" title="c28">c1'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c31">c2'</font>
 ;<br/>

<a NAME="E2:15_1_4_3_15_1"/>
<font color="Maroon" title="c26">c3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_15_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_15_1_1"/><i><font color="Green" title="E59">A154</font></i>: 
<font color="Maroon" title="c26">c3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font>
 ;<br/>

<a NAME="E2:15_1_4_3_15_1_1"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c25">c3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E3:15_1_4_3_15_1_1"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green" title="E34">A111</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_15_1_1"><i><font color="Green" title="E59">A154</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E4:15_1_4_3_15_1_1"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_3_15_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green" title="E32">A100</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:15_1_4_3_15_1"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c29">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c29">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E27:15_1_4_3"><i><font color="Green" title="E39">A120</font></i></a>, <a class="txt" href="conmetr.html#E36:15_1_4_3"><i><font color="Green" title="E43">A128</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_15_1"><i><font color="Green" title="E58">A153</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:15_1_4_3_15_1"/><b>then </b>
<font color="Maroon" title="c29">c1</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">c1</font>,<font color="Maroon" title="c3">a1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:15_1_4_3_15_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c29">c1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:15_1_4_3_15_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c28">c1'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c12">a1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:15_1_4_3_15_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c28">c1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E8:15_1_4_3_15_1"/><b>then </b><i><font color="Green" title="E59">A155</font></i>: 
<font color="Maroon" title="c28">c1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green" title="E25">A21</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E9:15_1_4_3_15_1"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c28">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c28">c1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E10:15_1_4_3_15_1"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E23:15_1_4_3"><i><font color="Green" title="E37">A118</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green" title="E44">A129</font></i></a>, <a class="txt" href="conmetr.html#E8:15_1_4_3_15_1"><i><font color="Green" title="E59">A155</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E11:15_1_4_3_15_1"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E12:15_1_4_3_15_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green" title="E32">A100</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:15_1_4_3_15"/><b>then </b>
<font color="Maroon" title="c16">b2'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c22">A'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E23:15_1_4_3"><i><font color="Green" title="E37">A118</font></i></a>, <a class="txt" href="conmetr.html#E32:15_1_4_3"><i><font color="Green" title="E41">A126</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_3_15"><i><font color="Green" title="E57">A152</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E5:15_1_4_3_15"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">N'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></i>;<br/>
<a NAME="E6:15_1_4_3_15"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c19">N'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E7:15_1_4_3_15"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c10">N</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E8:15_1_4_3_15"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green" title="E32">A100</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E55:15_1_4_3"/>
<font color="Maroon" title="c29">c1</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">c2</font>,<font color="Maroon" title="c4">a2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_16"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_3_16"/>
<font color="Maroon" title="c26">c3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_16_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_16_1"/><i><font color="Green" title="E57">A156</font></i>: 
<font color="Maroon" title="c26">c3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font>
 ;<br/>

<a NAME="E2:15_1_4_3_16_1"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E3:15_1_4_3_16_1"/><b>then </b>
<font color="Maroon" title="c22">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green" title="E30">A98</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green" title="E34">A111</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_16_1"><i><font color="Green" title="E57">A156</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E4:15_1_4_3_16_1"/><b>then </b>
<font color="Maroon" title="c23">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_3_16_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green" title="E32">A100</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:15_1_4_3_16"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c29">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c32">c2</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E27:15_1_4_3"><i><font color="Green" title="E39">A120</font></i></a>, <a class="txt" href="conmetr.html#E36:15_1_4_3"><i><font color="Green" title="E43">A128</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_3_16"/>
<font color="Maroon" title="c29">c1</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">c2</font>,<font color="Maroon" title="c4">a2</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E56:15_1_4_3"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:15"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green" title="E44">A129</font></i></a>, <a class="txt" href="conmetr.html#E40:15_1_4_3"><i><font color="Green" title="E47">A138</font></i></a>, <a class="txt" href="conmetr.html#E41:15_1_4_3"><i><font color="Green" title="E48">A139</font></i></a>, <a class="txt" href="conmetr.html#E52:15_1_4_3"><i><font color="Green" title="E54">A148</font></i></a>, <a class="txt" href="conmetr.html#E53:15_1_4_3"><i><font color="Green" title="E55">A149</font></i></a>, <a class="txt" href="conmetr.html#E54:15_1_4_3"><i><font color="Green" title="E56">A151</font></i></a>, <a class="ref" href="conaffm.html#D1" title="CONAFFM:def.1">CONAFFM:def 1</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:15_1_4"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4"><i><font color="Green" title="E27">A37</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:15_1"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:15_1"><i><font color="Green" title="E22">A8</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1"><i><font color="Green" title="E23">A13</font></i></a>, <a class="txt" href="conmetr.html#E4:15_1"><i><font color="Green" title="E24">A17</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:15"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="conmetr.html#D1" target="_self" title="CONMETR:def.1">Def1</a></i>;<br/>


</div>
