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<div class="add">

<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#V6" title="CONAFFM:attr.6">satisfying_LIN1</a>  implies <font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V7" title="CONAFFM:attr.7">satisfying_LIN2</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:5"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V6" title="CONAFFM:attr.6">satisfying_LIN1</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#V7" title="CONAFFM:attr.7">satisfying_LIN2</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#D7" target="_self" title="CONAFFM:def.7">CONAFFM:def 7</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="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> &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="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> holds <br/><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></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="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> &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="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> implies <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><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:5"/><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="E3:5"/><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="E4:5"/><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="E5:5"/><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="c6">b1</font>
 <span class="kw">and </span><br/><a NAME="E6:5"/><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="c7">c</font>
 <span class="kw">and </span><br/><a NAME="E7:5"/>
<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="E8:5"/><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="E9:5"/><span class="lab"><font color="Green" title="E12">A8</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>
 <span class="kw">and </span><br/><a NAME="E10:5"/><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="E11:5"/><span class="lab"><font color="Green" title="E14">A10</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="c6">b1</font>
 <span class="kw">and </span><br/><a NAME="E12:5"/><span class="lab"><font color="Green" title="E15">A11</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="E13:5"/><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="c3">a</font>,<font color="Maroon" title="c5">b</font>
 <span class="kw">and </span><br/><a NAME="E14:5"/><span class="lab"><font color="Green" title="E17">A13</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="E15:5"/><span class="lab"><font color="Green" title="E18">A14</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="E16:5"/><span class="lab"><font color="Green" title="E19">A15</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="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"> <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><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/>
<a NAME="E18:5"/>
 ex <font color="Olive" title="b1">c2</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="c4">a1</font>,<font color="Maroon" title="c8">c1</font>,<font color="Olive" title="b1">c2</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="Olive" title="b1">c2</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="b1">c2</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c16">e1</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="E2:5_1"/><span class="lab"><font color="Green" title="E20">A16</font></span>: 
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c16">e1</font>
 <span class="kw">and </span><br/><a NAME="E3:5_1"/><span class="lab"><font color="Green" title="E21">A17</font></span>: 
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">e1</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">e2</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="E5:5_1"/><span class="lab"><font color="Green" title="E22">A18</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="c17">e2</font>
 <span class="kw">and </span><br/><a NAME="E6:5_1"/><span class="lab"><font color="Green" title="E23">A19</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="c17">e2</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">reconsider </span><font color="Maroon" title="c18">e19</font> = <font color="Maroon" title="c16">e1</font>, <font color="Maroon" title="c19">e29</font> = <font color="Maroon" title="c17">e2</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="E8:5_1"/>
 not <font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c18">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c19">e29</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:5_1_1"/>
<font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c18">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o9</font>,<font color="Maroon" title="c19">e29</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="E2:5_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c16">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c17">e2</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="E3:5_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c17">e2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:5_1"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="txt" href="#E3:5_1"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E4:5_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A20</font></span>: 
<font color="Maroon" title="c4">a1</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="c7">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:5_1"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="txt" href="#E6:5_1"><span class="lab"><font color="Green" title="E23">A19</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E5:5_1_1"/>
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:5_1_1_1"/><span class="lab"><font color="Green" title="E25">A21</font></span>: 
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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"> contradiction</span><br/>

<a NAME="E2:5_1_1_1"/><span class="lab"><font color="Green" title="E26">A22</font></span>: 
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:5_1_1_1_1"/>
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="E2:5_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c5">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:5"><span class="lab"><font color="Green" title="E12">A8</font></span></a>, <a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E3:5_1_1_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</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="E4:5_1_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="c10">a19</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="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E5:5_1_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="c9">a9</font>,<font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c10">a19</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="E6:5_1_1_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c4">a1</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="E7:5_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A23</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</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="E8:5_1_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="#E13:5"><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="E9:5_1_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="c9">a9</font>,<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#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E10:5_1_1_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">o</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="E11:5_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</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="E12:5_1_1_1_1"/><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="c3">a</font>,<font color="Maroon" title="c5">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E13:5_1_1_1_1"/><span class="kw">then </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="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:5"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="txt" href="#E7:5_1_1_1_1"><span class="lab"><font color="Green" title="E27">A23</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E14:5_1_1_1_1"/><span class="kw">then </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="c3">a</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E15:5_1_1_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c2">o</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="E16:5_1_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="c9">a9</font>,<font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c15">o9</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="E17:5_1_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="c9">a9</font>,<font color="Maroon" title="c10">a19</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="E18:5_1_1_1_1"/><span class="kw">then </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="c4">a1</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="E19:5_1_1_1_1"/><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="E20:5_1_1_1_1"/><span class="kw">then </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="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:5"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E10:5"><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="E21:5_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:5"><span class="lab"><font color="Green" title="E6">A2</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="E3:5_1_1_1"/><span class="lab"><font color="Green" title="E27">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="c9">a9</font>,<font color="Maroon" title="c11">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:5"><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="E4:5_1_1_1"/><span class="lab"><font color="Green" title="E28">A25</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="#E14:5"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E5:5_1_1_1"/><span class="lab"><font color="Green" title="E29">A26</font></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="c15">o9</font>,<font color="Maroon" title="c9">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:5_1_1_1"><span class="lab"><font color="Green" title="E27">A24</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E6:5_1_1_1"/><span class="lab"><font color="Green" title="E30">A27</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">b19</font>,<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="#E4:5_1_1_1"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E7:5_1_1_1"/><span class="lab"><font color="Green" title="E31">A28</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<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="#E5:5_1_1_1"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E8:5_1_1_1"/><span class="lab"><font color="Green" title="E32">A29</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<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="#E6:5_1_1_1"><span class="lab"><font color="Green" title="E30">A27</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E9:5_1_1_1"/><span class="lab"><font color="Green" title="E33">A30</font></span>: 
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:5_1_1_1"><span class="lab"><font color="Green" title="E31">A28</font></span></a>, <a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/>
<a NAME="E10:5_1_1_1"/><span class="lab"><font color="Green" title="E34">A31</font></span>: 
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:5_1_1_1"><span class="lab"><font color="Green" title="E32">A29</font></span></a>, <a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/>
<a NAME="E11:5_1_1_1"/>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:5"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="ref" href="analmetr.html#T61" title="ANALMETR:th.61">ANALMETR:61</a></span>;<br/>
<a NAME="E12:5_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:5"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E9:5_1_1_1"><span class="lab"><font color="Green" title="E33">A30</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E13:5_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</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="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:5"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="txt" href="#E10:5_1_1_1"><span class="lab"><font color="Green" title="E34">A31</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E14:5_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="c5">b</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:5"><span class="lab"><font color="Green" title="E19">A15</font></span></a>, <a class="txt" href="#E1:5_1_1_1"><span class="lab"><font color="Green" title="E25">A21</font></span></a>, <a class="txt" href="#E2:5_1_1_1"><span class="lab"><font color="Green" title="E26">A22</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<a NAME="E15:5_1_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c3">a</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="E16:5_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="c9">a9</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="E17:5_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="c9">a9</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="E18:5_1_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</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="E19:5_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A32</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</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="E20:5_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="#E13:5"><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="E21:5_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="c9">a9</font>,<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#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E22:5_1_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">o</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="E23:5_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</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="E24:5_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:5"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="txt" href="#E19:5_1_1_1"><span class="lab"><font color="Green" title="E35">A32</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E25:5_1_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c2">o</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="E26:5_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="c9">a9</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="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E27:5_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#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E28:5_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:5"><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>; <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="E6:5_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</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="c7">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:5"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="txt" href="#E4:5_1_1"><span class="lab"><font color="Green" title="E24">A20</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<a NAME="E7:5_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E8:5_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c13">c9</font>,<font color="Maroon" title="c9">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E9:5_1_1"/><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="c9">a9</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="E10:5_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#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:5_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:5"><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>; <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="c20">c29</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="E10:5_1"/><span class="lab"><font color="Green" title="E24">A33</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c18">e19</font>,<font color="Maroon" title="c20">c29</font>
 <span class="kw">and </span><br/><a NAME="E11:5_1"/><span class="lab"><font color="Green" title="E25">A34</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="c19">e29</font>,<font color="Maroon" title="c20">c29</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">c2</font> = <font color="Maroon" title="c20">c29</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/>
<span class="kw">take </span>
<font color="Maroon" title="c21">c2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c21">c2</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="c21">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="c21">c2</font> )</span><br/>

<a NAME="E13:5_1"/>
<font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c18">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c20">c29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:5_1"><span class="lab"><font color="Green" title="E24">A33</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="E14:5_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c16">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c21">c2</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="E15:5_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A35</font></span>: 
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c21">c2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:5_1"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="txt" href="#E3:5_1"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E16:5_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c17">e2</font>,<font color="Maroon" title="c21">c2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:5_1"><span class="lab"><font color="Green" title="E25">A34</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E17:5_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A36</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c17">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c21">c2</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="E18:5_1"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:5_1_2"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c2</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="E2:5_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</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="txt" href="#E15:5_1"><span class="lab"><font color="Green" title="E26">A35</font></span></a>, <a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E3:5_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A37</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="c4">a1</font>,<font color="Maroon" title="c8">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:5"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E10:5"><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="E4:5_1_2"/>
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:5_1_2_1"/><span class="lab"><font color="Green" title="E29">A38</font></span>: 
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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"> contradiction</span><br/>

<a NAME="E2:5_1_2_1"/><span class="lab"><font color="Green" title="E30">A39</font></span>: 
<font color="Maroon" title="c4">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="5_1_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:5_1_2_1_1"/>
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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"> contradiction</span><br/>

<a NAME="E2:5_1_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c5">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:5"><span class="lab"><font color="Green" title="E12">A8</font></span></a>, <a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E3:5_1_2_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</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="E4:5_1_2_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">a19</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="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E5:5_1_2_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c10">a19</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="E6:5_1_2_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c4">a1</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="E7:5_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A40</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</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="E8:5_1_2_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="#E13:5"><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="E9:5_1_2_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a9</font>,<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#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E10:5_1_2_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">o</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="E11:5_1_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</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="E12:5_1_2_1_1"/><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="c3">a</font>,<font color="Maroon" title="c5">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E13:5_1_2_1_1"/><span class="kw">then </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="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:5"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="txt" href="#E7:5_1_2_1_1"><span class="lab"><font color="Green" title="E31">A40</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E14:5_1_2_1_1"/><span class="kw">then </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="c3">a</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E15:5_1_2_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c2">o</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="E16:5_1_2_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c15">o9</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="E17:5_1_2_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="c9">a9</font>,<font color="Maroon" title="c10">a19</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="E18:5_1_2_1_1"/><span class="kw">then </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="c4">a1</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="E19:5_1_2_1_1"/><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="E20:5_1_2_1_1"/><span class="kw">then </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="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:5"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E10:5"><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="E21:5_1_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:5"><span class="lab"><font color="Green" title="E6">A2</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="E3:5_1_2_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="c10">a19</font>,<font color="Maroon" title="c12">b19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:5"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E4:5_1_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">b19</font>,<font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c15">o9</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="E5:5_1_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c2">o</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="E6:5_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c2">o</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="E7:5_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</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="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E8:5_1_2_1"/><span class="kw">then </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="c2">o</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:5"><span class="lab"><font color="Green" title="E19">A15</font></span></a>, <a class="txt" href="#E1:5_1_2_1"><span class="lab"><font color="Green" title="E29">A38</font></span></a>, <a class="txt" href="#E2:5_1_2_1"><span class="lab"><font color="Green" title="E30">A39</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E9:5_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A41</font></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="#E5:5"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="txt" href="#E11:5"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<a NAME="E10:5_1_2_1"/><span class="lab"><font color="Green" title="E32">A42</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="#E13:5"><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="E11:5_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A43</font></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="c9">a9</font>,<font color="Maroon" title="c15">o9</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="E12:5_1_2_1"/><span class="lab"><font color="Green" title="E34">A44</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c15">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:5_1_2_1"><span class="lab"><font color="Green" title="E32">A42</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E13:5_1_2_1"/><span class="lab"><font color="Green" title="E35">A45</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:5_1_2_1"><span class="lab"><font color="Green" title="E33">A43</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E14:5_1_2_1"/><span class="lab"><font color="Green" title="E36">A46</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:5_1_2_1"><span class="lab"><font color="Green" title="E34">A44</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E15:5_1_2_1"/><span class="lab"><font color="Green" title="E37">A47</font></span>: 
<font color="Maroon" title="c5">b</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="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:5_1_2_1"><span class="lab"><font color="Green" title="E35">A45</font></span></a>, <a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/>
<a NAME="E16:5_1_2_1"/><span class="lab"><font color="Green" title="E38">A48</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:5_1_2_1"><span class="lab"><font color="Green" title="E36">A46</font></span></a>, <a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/>
<a NAME="E17:5_1_2_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:5_1_2_1"><span class="lab"><font color="Green" title="E37">A47</font></span></a>, <a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E18:5_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">b</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="#E4:5"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E9:5_1_2_1"><span class="lab"><font color="Green" title="E31">A41</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E19:5_1_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</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="E20:5_1_2_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="c9">a9</font>,<font color="Maroon" title="c13">c9</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="E21:5_1_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a9</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="E22:5_1_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</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="E23:5_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</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="E24:5_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:5"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="txt" href="#E16:5_1_2_1"><span class="lab"><font color="Green" title="E38">A48</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E25:5_1_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</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="E26:5_1_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a9</font>,<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="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E27:5_1_2_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#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E28:5_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:5"><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>; <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="E5:5_1_2"/><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="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:5"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="txt" href="#E3:5_1_2"><span class="lab"><font color="Green" title="E28">A37</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<a NAME="E6:5_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E7:5_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c2">o</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="E8:5_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a9</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="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E9:5_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#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:5_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:5"><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>; <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="E19:5_1"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c21">c2</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="c21">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="c21">c2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:5_1"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="txt" href="#E6:5_1"><span class="lab"><font color="Green" title="E23">A19</font></span></a>, <a class="txt" href="#E15:5_1"><span class="lab"><font color="Green" title="E26">A35</font></span></a>, <a class="txt" href="#E17:5_1"><span class="lab"><font color="Green" title="E27">A36</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</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">then </span><span class="kw">consider </span><font color="Maroon" title="c16">c2</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="E20:5"/><span class="lab"><font color="Green" title="E20">A49</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c16">c2</font>
 <span class="kw">and </span><br/><a NAME="E21:5"/><span class="lab"><font color="Green" title="E21">A50</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="c16">c2</font>
 <span class="kw">and </span><br/><a NAME="E22:5"/><span class="lab"><font color="Green" title="E22">A51</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">c2</font>
 ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">c29</font> = <font color="Maroon" title="c16">c2</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="E24:5"/><span class="lab"><font color="Green" title="E23">A52</font></span>: 
( <font color="Maroon" title="c5">b</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="c4">a1</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="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c1</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:5_2"/><span class="lab"><font color="Green" title="E24">A53</font></span>: 
( <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c</font> or <font color="Maroon" title="c4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font> or <font color="Maroon" title="c4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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"> contradiction</span><br/>

<div><span class="lab"><font color="Green" title="E25">A54</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="5_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:5_2_1"/>
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c</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="E2:5_2_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="c9">a9</font>,<font color="Maroon" title="c13">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:5"><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="E3:5_2_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#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/><span class="kw">hence </span><a NAME="E4:5_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:5"><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>; <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>
<div><span class="lab"><font color="Green" title="E26">A55</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="5_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:5_2_2"/>
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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"> contradiction</span><br/><a NAME="E2:5_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c5">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:5"><span class="lab"><font color="Green" title="E12">A8</font></span></a>, <a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E3:5_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</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="E4:5_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">a19</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="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E5:5_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c10">a19</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="E6:5_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c4">a1</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="E7:5_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A56</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</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="E8:5_2_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="#E13:5"><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="E9:5_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a9</font>,<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#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/><a NAME="E10:5_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">o</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="E11:5_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</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="E12:5_2_2"/><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="c3">a</font>,<font color="Maroon" title="c5">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E13:5_2_2"/><span class="kw">then </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="c2">o</font>,<font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:5"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="txt" href="#E7:5_2_2"><span class="lab"><font color="Green" title="E27">A56</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/><a NAME="E14:5_2_2"/><span class="kw">then </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="c3">a</font>,<font color="Maroon" title="c2">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E15:5_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c2">o</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="E16:5_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c15">o9</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="E17:5_2_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="c9">a9</font>,<font color="Maroon" title="c10">a19</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="E18:5_2_2"/><span class="kw">then </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="c4">a1</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="E19:5_2_2"/><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="E20:5_2_2"/><span class="kw">then </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="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:5"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E10:5"><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="E21:5_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:5"><span class="lab"><font color="Green" title="E6">A2</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>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_2_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:5_2_3"/><span class="lab"><font color="Green" title="E27">A57</font></span>: 
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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"> contradiction</span><br/><a NAME="E2:5_2_3"/>
 <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="#E14:5"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E3:5_2_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">b19</font>,<font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c15">o9</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="E4:5_2_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c2">o</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="E5:5_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c2">o</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="E6:5_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</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="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E7:5_2_3"/><span class="kw">then </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="c2">o</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:5"><span class="lab"><font color="Green" title="E19">A15</font></span></a>, <a class="txt" href="#E3:5_2"><span class="lab"><font color="Green" title="E26">A55</font></span></a>, <a class="txt" href="#E1:5_2_3"><span class="lab"><font color="Green" title="E27">A57</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/><a NAME="E8:5_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A58</font></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="#E5:5"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="txt" href="#E11:5"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/><a NAME="E9:5_2_3"/><span class="lab"><font color="Green" title="E29">A59</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="#E13:5"><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="E10:5_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A60</font></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="c9">a9</font>,<font color="Maroon" title="c15">o9</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="E11:5_2_3"/><span class="lab"><font color="Green" title="E31">A61</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c15">o9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:5_2_3"><span class="lab"><font color="Green" title="E29">A59</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/><a NAME="E12:5_2_3"/><span class="lab"><font color="Green" title="E32">A62</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:5_2_3"><span class="lab"><font color="Green" title="E30">A60</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E13:5_2_3"/><span class="lab"><font color="Green" title="E33">A63</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:5_2_3"><span class="lab"><font color="Green" title="E31">A61</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E14:5_2_3"/><span class="lab"><font color="Green" title="E34">A64</font></span>: 
<font color="Maroon" title="c5">b</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="c2">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:5_2_3"><span class="lab"><font color="Green" title="E32">A62</font></span></a>, <a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/><a NAME="E15:5_2_3"/><span class="lab"><font color="Green" title="E35">A65</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:5_2_3"><span class="lab"><font color="Green" title="E33">A63</font></span></a>, <a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/><a NAME="E16:5_2_3"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:5_2_3"><span class="lab"><font color="Green" title="E34">A64</font></span></a>, <a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E17:5_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c5">b</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="#E4:5"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E8:5_2_3"><span class="lab"><font color="Green" title="E28">A58</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/><a NAME="E18:5_2_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</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="E19:5_2_3"/><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="c9">a9</font>,<font color="Maroon" title="c13">c9</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="E20:5_2_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a9</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="E21:5_2_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</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="E22:5_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</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="E23:5_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:5"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="txt" href="#E15:5_2_3"><span class="lab"><font color="Green" title="E35">A65</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/><a NAME="E24:5_2_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</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="E25:5_2_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a9</font>,<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="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E26:5_2_3"/><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#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/><span class="kw">hence </span><a NAME="E27:5_2_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:5"><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>; <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="E5:5_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:5_2"><span class="lab"><font color="Green" title="E24">A53</font></span></a>, <a class="txt" href="#E2:5_2"><span class="lab"><font color="Green" title="E25">A54</font></span></a>, <a class="txt" href="#E3:5_2"><span class="lab"><font color="Green" title="E26">A55</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>
<a NAME="E25:5"/>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c16">c2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:5"><span class="lab"><font color="Green" title="E20">A49</font></span></a>, <a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/>
<a NAME="E26:5"/><span class="kw">then </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="c16">c2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:5"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="txt" href="#E24:5"><span class="lab"><font color="Green" title="E23">A52</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E27:5"/><span class="kw">then </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="c6">b1</font>,<font color="Maroon" title="c16">c2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:5"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="txt" href="#E2:5"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E3:5"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E4:5"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E5:5"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="txt" href="#E6:5"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="txt" href="#E8:5"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="txt" href="#E9:5"><span class="lab"><font color="Green" title="E12">A8</font></span></a>, <a class="txt" href="#E10:5"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="txt" href="#E11:5"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E12:5"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="txt" href="#E13:5"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="txt" href="#E14:5"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="txt" href="#E21:5"><span class="lab"><font color="Green" title="E21">A50</font></span></a>, <a class="txt" href="#E22:5"><span class="lab"><font color="Green" title="E22">A51</font></span></a>, <a class="ref" href="conaffm.html#D6" target="_self" title="CONAFFM:def.6">Def6</a></span>;<br/>
<a NAME="E28:5"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c16">c2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:5"><span class="lab"><font color="Green" title="E19">A15</font></span></a>, <a class="txt" href="#E24:5"><span class="lab"><font color="Green" title="E23">A52</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<a NAME="E29:5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A66</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c16">c2</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="E30:5"/>
 not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:5_3"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a1</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"> contradiction</span><br/>

<a NAME="E2:5_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">b19</font>,<font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c14">c19</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="E3:5_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c12">b19</font>,<font color="Maroon" title="c14">c19</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="E4:5_3"/><span class="kw">then </span>
<font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c12">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c14">c19</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="E5:5_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A67</font></span>: 
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</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="E6:5_3"/>
 <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="#E14:5"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E7:5_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c12">b19</font>,<font color="Maroon" title="c15">o9</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="E8:5_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c2">o</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="E9:5_3"/><span class="kw">then </span>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c2">o</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="E10:5_3"/><span class="kw">then </span>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:5"><span class="lab"><font color="Green" title="E23">A52</font></span></a>, <a class="txt" href="#E5:5_3"><span class="lab"><font color="Green" title="E25">A67</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E11:5_3"/><span class="kw">then </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="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:5"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="txt" href="#E24:5"><span class="lab"><font color="Green" title="E23">A52</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E12:5_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A68</font></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="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T61" title="ANALMETR:th.61">ANALMETR:61</a></span>;<br/>
<a NAME="E13:5_3"/>
<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="c3">a</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:5"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="ref" href="analmetr.html#T61" title="ANALMETR:th.61">ANALMETR:61</a></span>;<br/>
<a NAME="E14:5_3"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:5"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E12:5_3"><span class="lab"><font color="Green" title="E26">A68</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<a NAME="E15:5_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</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="E16:5_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a9</font>,<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="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E17:5_3"/><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#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:5_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:5"><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>; <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="E31:5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A69</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">b19</font>,<font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c14">c19</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="E32:5"/><span class="lab"><font color="Green" title="E26">A70</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">b19</font>,<font color="Maroon" title="c14">c19</font>,<font color="Maroon" title="c17">c29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:5"><span class="lab"><font color="Green" title="E24">A66</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E33:5"/>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c16">c2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:5"><span class="lab"><font color="Green" title="E20">A49</font></span></a>, <a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/>
<a NAME="E34:5"/><span class="kw">then </span>
<font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c14">c19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c17">c29</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/>
<span class="kw">hence </span><a NAME="E35:5"/>
<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">by</span> <span class="lab"><a class="txt" href="#E21:5"><span class="lab"><font color="Green" title="E21">A50</font></span></a>, <a class="txt" href="#E31:5"><span class="lab"><font color="Green" title="E25">A69</font></span></a>, <a class="txt" href="#E32:5"><span class="lab"><font color="Green" title="E26">A70</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</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>
