<?xml version="1.0"?>
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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V5" title="CONAFFM:attr.5">satisfying_LIN</a>  implies <font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V3" title="CONAFFM:attr.3">satisfying_3H</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:7"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V5" title="CONAFFM:attr.5">satisfying_LIN</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V3" title="CONAFFM:attr.3">satisfying_3H</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">a</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#D3" target="_self" title="CONAFFM:def.3">CONAFFM:def 3</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">b</font>, <font color="Olive" title="b2">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st  not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font> holds <br/> ex <font color="Olive" title="b3">d</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/>( <font color="Olive" title="b3">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font> &amp; <font color="Olive" title="b3">d</font>,<font color="Olive" title="b1">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b2">c</font> &amp; <font color="Olive" title="b3">d</font>,<font color="Olive" title="b2">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">b</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</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"> (  not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> implies  ex <font color="Olive" title="b1">d</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/>( <font color="Olive" title="b1">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Olive" title="b1">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Olive" title="b1">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E2:7"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
 not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">d</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/>( <font color="Olive" title="b1">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Olive" title="b1">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Olive" title="b1">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c5">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="E4:7"/><span class="lab"><font color="Green" title="E7">A3</font></span>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">e1</font>
 <span class="kw">and </span><br/><a NAME="E5:7"/><span class="lab"><font color="Green" title="E8">A4</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D9" title="ANALMETR:def.9">ANALMETR:def 9</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">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="E7:7"/><span class="lab"><font color="Green" title="E9">A5</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">e2</font>
 <span class="kw">and </span><br/><a NAME="E8:7"/><span class="lab"><font color="Green" title="E10">A6</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D9" title="ANALMETR:def.9">ANALMETR:def 9</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">a9</font> = <font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c8">b9</font> = <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c9">c9</font> = <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c10">e19</font> = <font color="Maroon" title="c5">e1</font>, <font color="Maroon" title="c11">e29</font> = <font color="Maroon" title="c6">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="E10:7"/>
 not <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c10">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c11">e29</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_1"/>
<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c10">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c11">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="E2:7_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">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="E3:7_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">e2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E5:7"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E4:7_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:7"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="txt" href="#E8:7"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<a NAME="E5:7_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c9">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E6:7_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c7">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c8">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E7:7_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E8:7_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">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/>
<span class="kw">hence </span><a NAME="E9:7_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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="c12">d9</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="E12:7"/><span class="lab"><font color="Green" title="E11">A7</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c10">e19</font>,<font color="Maroon" title="c12">d9</font>
 <span class="kw">and </span><br/><a NAME="E13:7"/><span class="lab"><font color="Green" title="E12">A8</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c11">e29</font>,<font color="Maroon" title="c12">d9</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="c13">d</font> = <font color="Maroon" title="c12">d9</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="c13">d</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="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )</span><br/>

<a NAME="E15:7"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">e2</font>,<font color="Maroon" title="c13">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:7"><span class="lab"><font color="Green" title="E12">A8</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E16:7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A9</font></span>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</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="E17:7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A10</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:7"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="txt" href="#E8:7"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E18:7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A11</font></span>: 
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">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="E19:7"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">e1</font>,<font color="Maroon" title="c13">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:7"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E20:7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A12</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</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="E21:7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A13</font></span>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E5:7"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E22:7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A14</font></span>: 
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="E23:7"/><span class="lab"><font color="Green" title="E19">A15</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V6" title="CONAFFM:attr.6">satisfying_LIN1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="conaffm.html#T3" target="_self" title="CONAFFM:th.3">Th3</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E20">A16</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:7_2"/><span class="lab"><font color="Green" title="E21">A17</font></span>: 
<font color="Maroon" title="c13">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</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="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )</span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:7_2_1"/><span class="lab"><font color="Green" title="E22">A18</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</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="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )</span><br/><a NAME="E2:7_2_1"/>
 not <font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c12">d9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c9">c9</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_1"/>
<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c12">d9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c9">c9</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="E2:7_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c9">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c12">d9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E3:7_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A19</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</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="E4:7_2_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">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="E2:7_2_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="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:7_2_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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="E5:7_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:7"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E3:7_2_1_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/>
<span class="kw">hence </span><a NAME="E6:7_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7_2_1"><span class="lab"><font color="Green" title="E22">A18</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><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">o9</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="E4:7_2_1"/><span class="lab"><font color="Green" title="E23">A20</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c12">d9</font>,<font color="Maroon" title="c14">o9</font>
 <span class="kw">and </span><br/><a NAME="E5:7_2_1"/><span class="lab"><font color="Green" title="E24">A21</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c14">o9</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="c15">o</font> = <font color="Maroon" title="c14">o9</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/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:7_2_1_2"/><span class="lab"><font color="Green" title="E25">A22</font></span>: 
<font color="Maroon" title="c13">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</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="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )</span><br/><a NAME="E2:7_2_1_2"/><span class="lab"><font color="Green" title="E26">A23</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_1"/><span class="lab"><font color="Green" title="E27">A24</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</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="E2:7_2_1_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7_2_1"><span class="lab"><font color="Green" title="E23">A20</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E3:7_2_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">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="E4:7_2_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:7"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E1:7_2_1"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E5:7_2_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A25</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">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="E6:7_2_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c12">d9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7_2_1"><span class="lab"><font color="Green" title="E23">A20</font></span></a>, <a class="txt" href="#E1:7_2_1_2_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="E7:7_2_1_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</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="E8:7_2_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A26</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</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="E9:7_2_1_2_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</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="E2:7_2_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="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:7_2_1_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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="E10:7_2_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7_2_1_2_1"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="#E8:7_2_1_2_1"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E11:7_2_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">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="E12:7_2_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:7"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="txt" href="#E1:7_2_1_2"><span class="lab"><font color="Green" title="E25">A22</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<a NAME="E13:7_2_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">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="E14:7_2_1_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">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="E15:7_2_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">c9</font>,<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">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="E16:7_2_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="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">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/>
<span class="kw">hence </span><a NAME="E17:7_2_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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="E3:7_2_1_2"/><span class="lab"><font color="Green" title="E27">A27</font></span>: 
<font color="Maroon" title="c4">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">o</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_2"/><span class="lab"><font color="Green" title="E28">A28</font></span>: 
<font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">o</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="E2:7_2_1_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7_2_1"><span class="lab"><font color="Green" title="E23">A20</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E3:7_2_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="E4:7_2_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A29</font></span>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:7"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E1:7_2_1"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E5:7_2_1_2_2"/>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_2_1"/>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">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="E2:7_2_1_2_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:7_2_1_2_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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="E6:7_2_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:7"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="txt" href="#E4:7_2_1_2_2"><span class="lab"><font color="Green" title="E29">A29</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<a NAME="E7:7_2_1_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">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="E8:7_2_1_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c12">d9</font>,<font color="Maroon" title="c9">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="E9:7_2_1_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">c9</font>,<font color="Maroon" title="c12">d9</font>,<font color="Maroon" title="c7">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E10:7_2_1_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</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="E11:7_2_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A30</font></span>: 
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">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="E12:7_2_1_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c12">d9</font>,<font color="Maroon" title="c8">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7_2_1"><span class="lab"><font color="Green" title="E23">A20</font></span></a>, <a class="txt" href="#E1:7_2_1_2_2"><span class="lab"><font color="Green" title="E28">A28</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E13:7_2_1_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</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="E14:7_2_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">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="E15:7_2_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7_2"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="txt" href="#E11:7_2_1_2_2"><span class="lab"><font color="Green" title="E30">A30</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E16:7_2_1_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">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="E17:7_2_1_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">c9</font>,<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">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="E18:7_2_1_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">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/>
<span class="kw">hence </span><a NAME="E19:7_2_1_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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">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="E5:7_2_1_2"/><span class="lab"><font color="Green" title="E28">A31</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c16">e1</font>
 <span class="kw">and </span><br/><a NAME="E6:7_2_1_2"/><span class="lab"><font color="Green" title="E29">A32</font></span>: 
<font color="Maroon" title="c2">a</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="E8:7_2_1_2"/><span class="lab"><font color="Green" title="E30">A33</font></span>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c17">e2</font>
 <span class="kw">and </span><br/><a NAME="E9:7_2_1_2"/><span class="lab"><font color="Green" title="E31">A34</font></span>: 
<font color="Maroon" title="c13">d</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="E11:7_2_1_2"/>
 not <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c18">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d9</font>,<font color="Maroon" title="c19">e29</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_3"/>
<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c18">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d9</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="E2:7_2_1_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c16">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</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="E3:7_2_1_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c17">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7_2_1_2"><span class="lab"><font color="Green" title="E28">A31</font></span></a>, <a class="txt" href="#E6:7_2_1_2"><span class="lab"><font color="Green" title="E29">A32</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E4:7_2_1_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:7_2_1_2"><span class="lab"><font color="Green" title="E30">A33</font></span></a>, <a class="txt" href="#E9:7_2_1_2"><span class="lab"><font color="Green" title="E31">A34</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E5:7_2_1_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">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="E6:7_2_1_2_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">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="E7:7_2_1_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">c9</font>,<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">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="E8:7_2_1_2_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">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/>
<span class="kw">hence </span><a NAME="E9:7_2_1_2_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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">d19</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="E13:7_2_1_2"/><span class="lab"><font color="Green" title="E32">A35</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c18">e19</font>,<font color="Maroon" title="c20">d19</font>
 <span class="kw">and </span><br/><a NAME="E14:7_2_1_2"/><span class="lab"><font color="Green" title="E33">A36</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d9</font>,<font color="Maroon" title="c19">e29</font>,<font color="Maroon" title="c20">d19</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">d1</font> = <font color="Maroon" title="c20">d19</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/><a NAME="E16:7_2_1_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c16">e1</font>,<font color="Maroon" title="c21">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:7_2_1_2"><span class="lab"><font color="Green" title="E32">A35</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E17:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c16">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c21">d1</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="E18:7_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A37</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c21">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7_2_1_2"><span class="lab"><font color="Green" title="E28">A31</font></span></a>, <a class="txt" href="#E6:7_2_1_2"><span class="lab"><font color="Green" title="E29">A32</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/><a NAME="E19:7_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A38</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c21">d1</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="E20:7_2_1_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c17">e2</font>,<font color="Maroon" title="c21">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:7_2_1_2"><span class="lab"><font color="Green" title="E33">A36</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E21:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c17">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c21">d1</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="E22:7_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A39</font></span>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c21">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:7_2_1_2"><span class="lab"><font color="Green" title="E30">A33</font></span></a>, <a class="txt" href="#E9:7_2_1_2"><span class="lab"><font color="Green" title="E31">A34</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/><a NAME="E23:7_2_1_2"/><span class="lab"><font color="Green" title="E37">A40</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_4"/><span class="lab"><font color="Green" title="E38">A41</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d</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="E2:7_2_1_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A42</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c15">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E5:7"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E20:7"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E3:7_2_1_2_4"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7_2_1"><span class="lab"><font color="Green" title="E24">A21</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E4:7_2_1_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c15">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="E5:7_2_1_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A43</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7_2_1_2"><span class="lab"><font color="Green" title="E26">A23</font></span></a>, <a class="txt" href="#E2:7_2_1_2_4"><span class="lab"><font color="Green" title="E39">A42</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E6:7_2_1_2_4"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_4_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_4_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">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="E2:7_2_1_2_4_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:7_2_1_2_4_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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="E7:7_2_1_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:7"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E1:7_2_1_2_4"><span class="lab"><font color="Green" title="E38">A41</font></span></a>, <a class="txt" href="#E5:7_2_1_2_4"><span class="lab"><font color="Green" title="E40">A43</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<a NAME="E8:7_2_1_2_4"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c4">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="E9:7_2_1_2_4"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c14">o9</font>,<font color="Maroon" title="c9">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="E10:7_2_1_2_4"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c14">o9</font>,<font color="Maroon" title="c8">b9</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="E11:7_2_1_2_4"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c3">b</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="E12:7_2_1_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A44</font></span>: 
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">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="E13:7_2_1_2_4"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c14">o9</font>,<font color="Maroon" title="c7">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7_2_1"><span class="lab"><font color="Green" title="E24">A21</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E14:7_2_1_2_4"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c2">a</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="E15:7_2_1_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">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="E16:7_2_1_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_2_1_2"><span class="lab"><font color="Green" title="E27">A27</font></span></a>, <a class="txt" href="#E12:7_2_1_2_4"><span class="lab"><font color="Green" title="E41">A44</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E17:7_2_1_2_4"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">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="E18:7_2_1_2_4"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c7">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="E19:7_2_1_2_4"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">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/>
<span class="kw">hence </span><a NAME="E20:7_2_1_2_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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="E24:7_2_1_2"/><span class="lab"><font color="Green" title="E38">A45</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_5"/><span class="lab"><font color="Green" title="E39">A46</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">d1</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="E2:7_2_1_2_5"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">o9</font>,<font color="Maroon" title="c12">d9</font>,<font color="Maroon" title="c8">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7_2_1"><span class="lab"><font color="Green" title="E23">A20</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E3:7_2_1_2_5"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</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="E4:7_2_1_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c3">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="E5:7_2_1_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c15">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="E6:7_2_1_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:7_2_1_2"><span class="lab"><font color="Green" title="E36">A39</font></span></a>, <a class="txt" href="#E23:7_2_1_2"><span class="lab"><font color="Green" title="E37">A40</font></span></a>, <a class="txt" href="#E1:7_2_1_2_5"><span class="lab"><font color="Green" title="E39">A46</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E7:7_2_1_2_5"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">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="E8:7_2_1_2_5"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c14">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="E9:7_2_1_2_5"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c14">o9</font>,<font color="Maroon" title="c8">b9</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="E10:7_2_1_2_5"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c3">b</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="E11:7_2_1_2_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A47</font></span>: 
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">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="E12:7_2_1_2_5"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c14">o9</font>,<font color="Maroon" title="c7">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7_2_1"><span class="lab"><font color="Green" title="E24">A21</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E13:7_2_1_2_5"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c2">a</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="E14:7_2_1_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">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="E15:7_2_1_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_2_1_2"><span class="lab"><font color="Green" title="E27">A27</font></span></a>, <a class="txt" href="#E11:7_2_1_2_5"><span class="lab"><font color="Green" title="E40">A47</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E16:7_2_1_2_5"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">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="E17:7_2_1_2_5"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">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="E18:7_2_1_2_5"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">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/>
<span class="kw">hence </span><a NAME="E19:7_2_1_2_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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="E25:7_2_1_2"/><span class="lab"><font color="Green" title="E39">A48</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_6"/>
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</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="E2:7_2_1_2_6"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7_2_1"><span class="lab"><font color="Green" title="E24">A21</font></span></a>, <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="E3:7_2_1_2_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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="E26:7_2_1_2"/><span class="lab"><font color="Green" title="E40">A49</font></span>: 
<font color="Maroon" title="c21">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_7"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_7"/><span class="lab"><font color="Green" title="E41">A50</font></span>: 
<font color="Maroon" title="c21">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">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="E2:7_2_1_2_7"/><span class="lab"><font color="Green" title="E42">A51</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_7_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_7_1"/>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">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="E2:7_2_1_2_7_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:7_2_1_2_7_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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="E3:7_2_1_2_7"/>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:7_2_1_2"><span class="lab"><font color="Green" title="E36">A39</font></span></a>, <a class="txt" href="#E1:7_2_1_2_7"><span class="lab"><font color="Green" title="E41">A50</font></span></a>, <a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E4:7_2_1_2_7"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</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="E5:7_2_1_2_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A52</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c12">d9</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="E6:7_2_1_2_7"/>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:7_2_1_2"><span class="lab"><font color="Green" title="E36">A39</font></span></a>, <a class="txt" href="#E1:7_2_1_2_7"><span class="lab"><font color="Green" title="E41">A50</font></span></a>, <a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E7:7_2_1_2_7"/><span class="kw">then </span>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:7"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="txt" href="#E2:7_2_1_2_7"><span class="lab"><font color="Green" title="E42">A51</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E8:7_2_1_2_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A53</font></span>: 
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</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="E9:7_2_1_2_7"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d9</font>,<font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c8">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7_2_1_2_7"><span class="lab"><font color="Green" title="E43">A52</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E10:7_2_1_2_7"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</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="E11:7_2_1_2_7"/><span class="kw">then </span>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">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="E12:7_2_1_2_7"/><span class="kw">then </span>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7_2"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="txt" href="#E8:7_2_1_2_7"><span class="lab"><font color="Green" title="E44">A53</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E13:7_2_1_2_7"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:7"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="txt" href="#E1:7_2_1"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<a NAME="E14:7_2_1_2_7"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</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="E15:7_2_1_2_7"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</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="E16:7_2_1_2_7"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c12">d9</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="E17:7_2_1_2_7"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c12">d9</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="E18:7_2_1_2_7"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</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="E19:7_2_1_2_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A54</font></span>: 
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</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="E20:7_2_1_2_7"/>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:7_2_1_2"><span class="lab"><font color="Green" title="E36">A39</font></span></a>, <a class="txt" href="#E1:7_2_1_2_7"><span class="lab"><font color="Green" title="E41">A50</font></span></a>, <a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E21:7_2_1_2_7"/><span class="kw">then </span>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7_2"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="txt" href="#E19:7_2_1_2_7"><span class="lab"><font color="Green" title="E45">A54</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E22:7_2_1_2_7"/><span class="kw">then </span>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">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="E23:7_2_1_2_7"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">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="E24:7_2_1_2_7"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">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="E25:7_2_1_2_7"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">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/>
<span class="kw">hence </span><a NAME="E26:7_2_1_2_7"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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="E27:7_2_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d9</font>,<font color="Maroon" title="c14">o9</font>,<font color="Maroon" title="c8">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7_2_1"><span class="lab"><font color="Green" title="E23">A20</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/><a NAME="E28:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c12">d9</font>,<font color="Maroon" title="c14">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d9</font>,<font color="Maroon" title="c8">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E29:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c12">d9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">o9</font>,<font color="Maroon" title="c12">d9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><a NAME="E30:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</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="E31:7_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A55</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:7"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E1:7_2_1"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/><a NAME="E32:7_2_1_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7_2_1"><span class="lab"><font color="Green" title="E24">A21</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E33:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c15">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="E34:7_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A56</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c2">a</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="E35:7_2_1_2"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_8"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_8"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">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="E2:7_2_1_2_8"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:7_2_1_2_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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="E36:7_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A57</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c2">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:7_2_1_2"><span class="lab"><font color="Green" title="E41">A55</font></span></a>, <a class="txt" href="#E34:7_2_1_2"><span class="lab"><font color="Green" title="E42">A56</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/><a NAME="E37:7_2_1_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7_2_1"><span class="lab"><font color="Green" title="E24">A21</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E38:7_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A58</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c15">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="E39:7_2_1_2"/><span class="lab"><font color="Green" title="E45">A59</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_9"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_9"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">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="E2:7_2_1_2_9"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:7_2_1_2_9"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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="E40:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c21">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:7_2_1_2"><span class="lab"><font color="Green" title="E34">A37</font></span></a>, <a class="txt" href="#E38:7_2_1_2"><span class="lab"><font color="Green" title="E44">A58</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/><a NAME="E41:7_2_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">d1</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="E42:7_2_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c14">o9</font>,<font color="Maroon" title="c20">d19</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="E43:7_2_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">o9</font>,<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c20">d19</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="E44:7_2_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c21">d1</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="E45:7_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A60</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">d1</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="E46:7_2_1_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7_2_1"><span class="lab"><font color="Green" title="E24">A21</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E47:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c15">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="E48:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</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="E49:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7_2_1_2"><span class="lab"><font color="Green" title="E26">A23</font></span></a>, <a class="txt" href="#E45:7_2_1_2"><span class="lab"><font color="Green" title="E46">A60</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/><a NAME="E50:7_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A61</font></span>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:7"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E39:7_2_1_2"><span class="lab"><font color="Green" title="E45">A59</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/><a NAME="E51:7_2_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d9</font>,<font color="Maroon" title="c14">o9</font>,<font color="Maroon" title="c8">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7_2_1"><span class="lab"><font color="Green" title="E23">A20</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/><a NAME="E52:7_2_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c3">b</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="E53:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">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="E54:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</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="E55:7_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A62</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">d1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7_2_1"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="txt" href="#E50:7_2_1_2"><span class="lab"><font color="Green" title="E47">A61</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/><a NAME="E56:7_2_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c14">o9</font>,<font color="Maroon" title="c7">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7_2_1"><span class="lab"><font color="Green" title="E24">A21</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/><a NAME="E57:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c14">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c7">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E58:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c9">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">o9</font>,<font color="Maroon" title="c9">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><a NAME="E59:7_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A63</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c4">c</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="E60:7_2_1_2"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_10"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_10"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">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="E2:7_2_1_2_10"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:7_2_1_2_10"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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="E61:7_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A64</font></span>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:7"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E59:7_2_1_2"><span class="lab"><font color="Green" title="E49">A63</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/><a NAME="E62:7_2_1_2"/>
<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c12">d9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c14">o9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7_2_1"><span class="lab"><font color="Green" title="E23">A20</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="E63:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c12">d9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">o9</font>,<font color="Maroon" title="c8">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><a NAME="E64:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c3">b</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="E65:7_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A65</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c3">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7_2_1"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="txt" href="#E61:7_2_1_2"><span class="lab"><font color="Green" title="E50">A64</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/><a NAME="E66:7_2_1_2"/><span class="lab"><font color="Green" title="E52">A66</font></span>: 
 not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c21">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_11"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_11"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c21">d1</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="E2:7_2_1_2_11"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">d1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/>
<a NAME="E3:7_2_1_2_11"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:7_2_1_2"><span class="lab"><font color="Green" title="E38">A45</font></span></a>, <a class="txt" href="#E55:7_2_1_2"><span class="lab"><font color="Green" title="E48">A62</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:7_2_1_2_11"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:7_2_1_2"><span class="lab"><font color="Green" title="E37">A40</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="E67:7_2_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c20">d19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:7_2_1_2"><span class="lab"><font color="Green" title="E35">A38</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E68:7_2_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">c9</font>,<font color="Maroon" title="c20">d19</font>,<font color="Maroon" title="c7">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/><a NAME="E69:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c20">d19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c7">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E70:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c9">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c20">d19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><a NAME="E71:7_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A67</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c21">d1</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="E72:7_2_1_2"/><span class="lab"><font color="Green" title="E54">A68</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_12"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_12"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">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="E2:7_2_1_2_12"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:7_2_1_2_12"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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="E73:7_2_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c14">o9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7_2_1"><span class="lab"><font color="Green" title="E24">A21</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/><a NAME="E74:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c7">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c14">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="E75:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c9">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c9</font>,<font color="Maroon" title="c14">o9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><a NAME="E76:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</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="E77:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c21">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E71:7_2_1_2"><span class="lab"><font color="Green" title="E53">A67</font></span></a>, <a class="txt" href="#E72:7_2_1_2"><span class="lab"><font color="Green" title="E54">A68</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/><a NAME="E78:7_2_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c15">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="E79:7_2_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">c9</font>,<font color="Maroon" title="c20">d19</font>,<font color="Maroon" title="c14">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="E80:7_2_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">o9</font>,<font color="Maroon" title="c20">d19</font>,<font color="Maroon" title="c9">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="E81:7_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A69</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c4">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="E82:7_2_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">o9</font>,<font color="Maroon" title="c12">d9</font>,<font color="Maroon" title="c8">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7_2_1"><span class="lab"><font color="Green" title="E23">A20</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/><a NAME="E83:7_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A70</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</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="E84:7_2_1_2"/><span class="lab"><font color="Green" title="E57">A71</font></span>: 
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:7_2_1_2"><span class="lab"><font color="Green" title="E36">A39</font></span></a>, <a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E85:7_2_1_2"/>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2_13"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_2_1_2_13"/>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">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="E2:7_2_1_2_13"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c9">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:7_2_1_2_13"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E6">A2</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="E86:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c21">d1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:7"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="txt" href="#E22:7_2_1_2"><span class="lab"><font color="Green" title="E36">A39</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/><a NAME="E87:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</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="E88:7_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:7"><span class="lab"><font color="Green" title="E19">A15</font></span></a>, <a class="txt" href="#E2:7_2_1_2"><span class="lab"><font color="Green" title="E26">A23</font></span></a>, <a class="txt" href="#E3:7_2_1_2"><span class="lab"><font color="Green" title="E27">A27</font></span></a>, <a class="txt" href="#E23:7_2_1_2"><span class="lab"><font color="Green" title="E37">A40</font></span></a>, <a class="txt" href="#E24:7_2_1_2"><span class="lab"><font color="Green" title="E38">A45</font></span></a>, <a class="txt" href="#E25:7_2_1_2"><span class="lab"><font color="Green" title="E39">A48</font></span></a>, <a class="txt" href="#E26:7_2_1_2"><span class="lab"><font color="Green" title="E40">A49</font></span></a>, <a class="txt" href="#E36:7_2_1_2"><span class="lab"><font color="Green" title="E43">A57</font></span></a>, <a class="txt" href="#E55:7_2_1_2"><span class="lab"><font color="Green" title="E48">A62</font></span></a>, <a class="txt" href="#E65:7_2_1_2"><span class="lab"><font color="Green" title="E51">A65</font></span></a>, <a class="txt" href="#E66:7_2_1_2"><span class="lab"><font color="Green" title="E52">A66</font></span></a>, <a class="txt" href="#E81:7_2_1_2"><span class="lab"><font color="Green" title="E55">A69</font></span></a>, <a class="txt" href="#E83:7_2_1_2"><span class="lab"><font color="Green" title="E56">A70</font></span></a>, <a class="txt" href="#E84:7_2_1_2"><span class="lab"><font color="Green" title="E57">A71</font></span></a>, <a class="ref" href="conaffm.html#D6" target="_self" title="CONAFFM:def.6">Def6</a></span>;<br/><span class="kw">hence </span><a NAME="E89:7_2_1_2"/>
( <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:7"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E21:7"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="ref" href="analmetr.html#T61" title="ANALMETR:th.61">ANALMETR:61</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E8:7_2_1"/>
( <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E5:7"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E17:7"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E20:7"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="ref" href="analmetr.html#T61" title="ANALMETR:th.61">ANALMETR:61</a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</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="E3:7_2"/>
( <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:7"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="txt" href="#E8:7"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="txt" href="#E16:7"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="txt" href="#E21:7"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="ref" href="analmetr.html#T61" title="ANALMETR:th.61">ANALMETR:61</a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</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="7_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:7_3"/>
<font color="Maroon" title="c13">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</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="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )</span><br/><a NAME="E2:7_3"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</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">hence </span><a NAME="E3:7_3"/>
( <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:7"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E21:7"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="ref" href="analmetr.html#T61" title="ANALMETR:th.61">ANALMETR:61</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E26:7"/>
( <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:7"><span class="lab"><font color="Green" title="E20">A16</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>
