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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V5" title="CONAFFM:attr.5">satisfying_LIN</a>  implies <font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V6" title="CONAFFM:attr.6">satisfying_LIN1</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:4"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V5" title="CONAFFM:attr.5">satisfying_LIN</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V6" title="CONAFFM:attr.6">satisfying_LIN1</a> </span><br/>

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













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:4"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">and </span><br/><a NAME="E3:4"/><span class="lab"><font color="Green" title="E7">A3</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a1</font>
 <span class="kw">and </span><br/><a NAME="E4:4"/><span class="lab"><font color="Green" title="E8">A4</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b</font>
 <span class="kw">and </span><br/><a NAME="E5:4"/>
<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>
 <span class="kw">and </span><br/><a NAME="E6:4"/><span class="lab"><font color="Green" title="E9">A5</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">c</font>
 <span class="kw">and </span><br/><a NAME="E7:4"/><span class="lab"><font color="Green" title="E10">A6</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c1</font>
 <span class="kw">and </span><br/><a NAME="E8:4"/><span class="lab"><font color="Green" title="E11">A7</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b</font>
 <span class="kw">and </span><br/><a NAME="E9:4"/><span class="lab"><font color="Green" title="E12">A8</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font>
 <span class="kw">and </span><br/><a NAME="E10:4"/><span class="lab"><font color="Green" title="E13">A9</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>
 <span class="kw">and </span><br/><a NAME="E11:4"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">and </span><br/><a NAME="E12:4"/><span class="lab"><font color="Green" title="E14">A10</font></span>: 
 not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c3">a</font>
 <span class="kw">and </span><br/><a NAME="E13:4"/><span class="lab"><font color="Green" title="E15">A11</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>
 <span class="kw">and </span><br/><a NAME="E14:4"/><span class="lab"><font color="Green" title="E16">A12</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">and </span><br/><a NAME="E15:4"/><span class="lab"><font color="Green" title="E17">A13</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font>
 <span class="kw">and </span><br/><a NAME="E16:4"/><span class="lab"><font color="Green" title="E18">A14</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c9">a9</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c10">a19</font> = <font color="Maroon" title="c4">a1</font>, <font color="Maroon" title="c11">b9</font> = <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c12">b19</font> = <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c13">c9</font> = <font color="Maroon" title="c7">c</font>, <font color="Maroon" title="c14">c19</font> = <font color="Maroon" title="c8">c1</font>, <font color="Maroon" title="c15">o9</font> = <font color="Maroon" title="c2">o</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:4_1"/>
 ex <font color="Olive" title="b1">b2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Olive" title="b1">b2</font> &amp; <font color="Maroon" title="c8">c1</font>,<font color="Olive" title="b1">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c8">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">b2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c16">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:4_1_1"/><span class="lab"><font color="Green" title="E19">A15</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">y</font>
 <span class="kw">and </span><br/><a NAME="E3:4_1_1"/><span class="lab"><font color="Green" title="E20">A16</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T39" title="ANALMETR:th.39">ANALMETR:39</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c17">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E5:4_1_1"/><span class="lab"><font color="Green" title="E21">A17</font></span>: 
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c17">x</font>
 <span class="kw">and </span><br/><a NAME="E6:4_1_1"/><span class="lab"><font color="Green" title="E22">A18</font></span>: 
<font color="Maroon" title="c8">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T39" title="ANALMETR:th.39">ANALMETR:39</a></span>;<br/>
<a NAME="E7:4_1_1"/><span class="lab"><font color="Green" title="E23">A19</font></span>: 
 not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c17">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:4_1_1_1"/><span class="lab"><font color="Green" title="E24">A20</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c17">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c18">y9</font> = <font color="Maroon" title="c16">y</font>, <font color="Maroon" title="c19">x9</font> = <font color="Maroon" title="c17">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/>
<a NAME="E3:4_1_1_1"/><span class="lab"><font color="Green" title="E25">A21</font></span>: 
<font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c18">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c19</font>,<font color="Maroon" title="c19">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:4_1_1_1"><span class="lab"><font color="Green" title="E24">A20</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E4:4_1_1_1"/>
<font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c10">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c18">y9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4_1_1"><span class="lab"><font color="Green" title="E19">A15</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E5:4_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c18">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c10">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E6:4_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">c19</font>,<font color="Maroon" title="c19">x9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c10">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:4_1_1"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="txt" href="#E3:4_1_1_1"><span class="lab"><font color="Green" title="E25">A21</font></span></a>, <a class="ref" href="diraf.html#T40" title="DIRAF:th.40">DIRAF:40</a></span>;<br/>
<a NAME="E7:4_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c17">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E8:4_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:4_1_1"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="txt" href="#E6:4_1_1"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E9:4_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A22</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:4"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E10:4"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<a NAME="E10:4_1_1_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:4"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/>
<a NAME="E11:4_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E9:4_1_1_1"><span class="lab"><font color="Green" title="E26">A22</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E12:4_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c13">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c11">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E13:4_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c13">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c15">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E14:4_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c13">c9</font>,<font color="Maroon" title="c15">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E15:4_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c13">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E16:4_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A23</font></span>: 
<font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c11">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c13">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E17:4_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c11">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:4"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E18:4_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c9">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E19:4_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c11">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c9">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E20:4_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c13">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c9">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:4"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E16:4_1_1_1"><span class="lab"><font color="Green" title="E27">A23</font></span></a>, <a class="ref" href="diraf.html#T40" title="DIRAF:th.40">DIRAF:40</a></span>;<br/>
<a NAME="E21:4_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c13">c9</font>,<font color="Maroon" title="c9">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E22:4_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:4"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">reconsider </span><font color="Maroon" title="c18">y9</font> = <font color="Maroon" title="c16">y</font>, <font color="Maroon" title="c19">x9</font> = <font color="Maroon" title="c17">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/>
<a NAME="E9:4_1_1"/>
 not <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c18">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c19</font>,<font color="Maroon" title="c19">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:4_1_1"><span class="lab"><font color="Green" title="E23">A19</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c20">b29</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><span class="kw"> such that </span><br/><a NAME="E11:4_1_1"/><span class="lab"><font color="Green" title="E24">A24</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c18">y9</font>,<font color="Maroon" title="c20">b29</font>
 <span class="kw">and </span><br/><a NAME="E12:4_1_1"/><span class="lab"><font color="Green" title="E25">A25</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">c19</font>,<font color="Maroon" title="c19">x9</font>,<font color="Maroon" title="c20">b29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T60" title="AFF_1:th.60">AFF_1:60</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c21">b2</font> = <font color="Maroon" title="c20">b29</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/>
<a NAME="E14:4_1_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c21">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:4_1_1"><span class="lab"><font color="Green" title="E25">A25</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E15:4_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c17">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c21">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/>
<a NAME="E16:4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A26</font></span>: 
<font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c21">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:4_1_1"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="txt" href="#E6:4_1_1"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E17:4_1_1"/>
<font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c10">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c18">y9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4_1_1"><span class="lab"><font color="Green" title="E19">A15</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E18:4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A27</font></span>: 
<font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c18">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c10">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E19:4_1_1"/>
<font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c18">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c20">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:4_1_1"><span class="lab"><font color="Green" title="E24">A24</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E20:4_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c10">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c20">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:4_1_1"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="txt" href="#E18:4_1_1"><span class="lab"><font color="Green" title="E27">A27</font></span></a>, <a class="ref" href="diraf.html#T40" title="DIRAF:th.40">DIRAF:40</a></span>;<br/>
<a NAME="E21:4_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c20">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E22:4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A28</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c21">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E23:4_1_1"/>
<font color="Maroon" title="c8">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">b2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:4_1_1_2"/>
<font color="Maroon" title="c8">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:4_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:4_1_1"><span class="lab"><font color="Green" title="E28">A28</font></span></a>, <a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/>
<a NAME="E3:4_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:4"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E10:4"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E4:4_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:4"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="txt" href="#E9:4"><span class="lab"><font color="Green" title="E12">A8</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:4_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:4"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E24:4_1_1"/>
 ex <font color="Olive" title="b1">b2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Olive" title="b1">b2</font> &amp; <font color="Maroon" title="c8">c1</font>,<font color="Olive" title="b1">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c8">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">b2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:4_1_1"><span class="lab"><font color="Green" title="E26">A26</font></span></a>, <a class="txt" href="#E22:4_1_1"><span class="lab"><font color="Green" title="E28">A28</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c16">b2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E3:4_1"/><span class="lab"><font color="Green" title="E19">A29</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c16">b2</font>
 <span class="kw">and </span><br/><a NAME="E4:4_1"/><span class="lab"><font color="Green" title="E20">A30</font></span>: 
<font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c16">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 <span class="kw">and </span><br/><a NAME="E5:4_1"/>
<font color="Maroon" title="c8">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">b2</font>
 ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c17">b29</font> = <font color="Maroon" title="c16">b2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/><a NAME="E7:4_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:4_1"><span class="lab"><font color="Green" title="E19">A29</font></span></a>, <a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/><a NAME="E8:4_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A31</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:4"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E10:4"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/><a NAME="E9:4_1"/><span class="lab"><font color="Green" title="E22">A32</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:4"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/><a NAME="E10:4_1"/><span class="lab"><font color="Green" title="E23">A33</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">b2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:4_1_2"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:4_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:4_1"><span class="lab"><font color="Green" title="E20">A30</font></span></a>, <a class="ref" href="analmetr.html#T61" title="ANALMETR:th.61">ANALMETR:61</a></span>;<br/>
<a NAME="E3:4_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:4"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="txt" href="#E9:4"><span class="lab"><font color="Green" title="E12">A8</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<a NAME="E4:4_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c13">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c13">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E5:4_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c13">c9</font>,<font color="Maroon" title="c15">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">c9</font>,<font color="Maroon" title="c11">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E6:4_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">c9</font>,<font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c11">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E7:4_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c13">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E8:4_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A34</font></span>: 
<font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c11">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c13">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E9:4_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c11">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:4"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E10:4_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c9">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E11:4_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c11">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c9">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E12:4_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c13">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c9">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:4"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E8:4_1_2"><span class="lab"><font color="Green" title="E24">A34</font></span></a>, <a class="ref" href="diraf.html#T40" title="DIRAF:th.40">DIRAF:40</a></span>;<br/>
<a NAME="E13:4_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c13">c9</font>,<font color="Maroon" title="c9">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:4_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:4"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E11:4_1"/><span class="lab"><font color="Green" title="E24">A35</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E8:4_1"><span class="lab"><font color="Green" title="E21">A31</font></span></a>, <a class="txt" href="#E9:4_1"><span class="lab"><font color="Green" title="E22">A32</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/><a NAME="E12:4_1"/>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c16">b2</font>,<font color="Maroon" title="c8">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:4_1"><span class="lab"><font color="Green" title="E20">A30</font></span></a>, <a class="ref" href="analmetr.html#T61" title="ANALMETR:th.61">ANALMETR:61</a></span>;<br/><a NAME="E13:4_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A36</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c16">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:4"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E3:4"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E4:4"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E6:4"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="txt" href="#E7:4"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="txt" href="#E8:4"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="txt" href="#E9:4"><span class="lab"><font color="Green" title="E12">A8</font></span></a>, <a class="txt" href="#E10:4"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="txt" href="#E12:4"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E13:4"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="txt" href="#E15:4"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="txt" href="#E3:4_1"><span class="lab"><font color="Green" title="E19">A29</font></span></a>, <a class="txt" href="#E10:4_1"><span class="lab"><font color="Green" title="E23">A33</font></span></a>, <a class="txt" href="#E11:4_1"><span class="lab"><font color="Green" title="E24">A35</font></span></a>, <a class="ref" href="conaffm.html#D5" target="_self" title="CONAFFM:def.5">Def5</a></span>;<br/><a NAME="E14:4_1"/>
 not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:4_1_3"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:4_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/>
<a NAME="E3:4_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E10:4"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:4_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:4"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="ref" href="analmetr.html#T39" title="ANALMETR:th.39">ANALMETR:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E15:4_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A37</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E16:4_1"/><span class="lab"><font color="Green" title="E27">A38</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c11">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:4"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E17:4_1"/><span class="lab"><font color="Green" title="E28">A39</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c12">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:4"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E18:4_1"/><span class="lab"><font color="Green" title="E29">A40</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c17">b29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:4_1"><span class="lab"><font color="Green" title="E19">A29</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E19:4_1"/><span class="lab"><font color="Green" title="E30">A41</font></span>: 
<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c12">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:4"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E20:4_1"/>
<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c17">b29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:4_1"><span class="lab"><font color="Green" title="E25">A36</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E21:4_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:4_1"><span class="lab"><font color="Green" title="E26">A37</font></span></a>, <a class="txt" href="#E16:4_1"><span class="lab"><font color="Green" title="E27">A38</font></span></a>, <a class="txt" href="#E17:4_1"><span class="lab"><font color="Green" title="E28">A39</font></span></a>, <a class="txt" href="#E18:4_1"><span class="lab"><font color="Green" title="E29">A40</font></span></a>, <a class="txt" href="#E19:4_1"><span class="lab"><font color="Green" title="E30">A41</font></span></a>, <a class="ref" href="aff_1.html#T56" title="AFF_1:th.56">AFF_1:56</a></span>;<br/><span class="kw">hence </span><a NAME="E22:4_1"/>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:4_1"><span class="lab"><font color="Green" title="E20">A30</font></span></a>, <a class="ref" href="analmetr.html#T61" title="ANALMETR:th.61">ANALMETR:61</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E19:4"/>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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