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<span class="kw">let </span><font color="Maroon" title="c7">POS</font> be   <a href="analmetr.html#NM1" title="ANALMETR:NM.1">OrtAfSp</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font> is   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a> implies <font color="Maroon" title="c7">POS</font> is   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a> )</span><br/>

<span class="kw">assume </span><a NAME="E1:75"/><span class="lab"><font color="Green" title="E49">A1</font></span>: 
 <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font> is   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">POS</font> is   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a></span><br/>

<div><span class="lab"><font color="Green" title="E50">A2</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c9">b</font>, <font color="Maroon" title="c10">c</font>, <font color="Maroon" title="c11">d</font>, <font color="Maroon" title="c12">p</font>, <font color="Maroon" title="c13">q</font>, <font color="Maroon" title="c14">r</font>, <font color="Maroon" title="c15">s</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> implies <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b</font> ) &amp; <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c10">c</font> &amp; ( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c11">d</font> implies ( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c10">c</font> &amp; <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c11">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> ) ) &amp; ( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> &amp; <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> &amp; not <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> implies <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b</font> ) &amp; ( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> &amp; <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> &amp; not <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> implies <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b</font> ) )</span><br/><span class="kw">thus </span><a NAME="E1:75_1"/>
( ( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> implies <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b</font> ) &amp; <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c10">c</font> &amp; ( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c11">d</font> implies ( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c10">c</font> &amp; <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c11">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> ) ) &amp; ( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> &amp; <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> &amp; not <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> implies <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> &amp; <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> &amp; not <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> implies <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b</font> )</span><br/><span class="kw">thus </span><a NAME="E2:75_1"/>
( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> &amp; <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> &amp; not <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> implies <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b</font> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c16">a9</font> = <font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c17">b9</font> = <font color="Maroon" title="c9">b</font>, <font color="Maroon" title="c18">p9</font> = <font color="Maroon" title="c12">p</font>, <font color="Maroon" title="c19">q9</font> = <font color="Maroon" title="c13">q</font>, <font color="Maroon" title="c20">r9</font> = <font color="Maroon" title="c14">r</font>, <font color="Maroon" title="c21">s9</font> = <font color="Maroon" title="c15">s</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font></span>)</span> ;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:75_1_1"/><span class="lab"><font color="Green" title="E51">A3</font></span>: 
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font>
 <span class="kw">and </span><br/><a NAME="E3:75_1_1"/><span class="lab"><font color="Green" title="E52">A4</font></span>: 
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> or <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b</font> )</span><br/>

<a NAME="E4:75_1_1"/><span class="lab"><font color="Green" title="E53">A5</font></span>: 
<font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:75_1_1"><span class="lab"><font color="Green" title="E51">A3</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/>
<a NAME="E5:75_1_1"/><span class="lab"><font color="Green" title="E54">A6</font></span>: 
<font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:75_1_1"><span class="lab"><font color="Green" title="E52">A4</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/>
<span class="kw">assume </span><a NAME="E6:75_1_1"/><span class="lab"><font color="Green" title="E55">A7</font></span>: 
( not <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> &amp; not <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E7:75_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A8</font></span>: 
not <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c19">q9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/>
<a NAME="E8:75_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A9</font></span>: 
<font color="Maroon" title="c18">p9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">q9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T12" title="AFF_1:th.12">AFF_1:12</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c22">x9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E10:75_1_1"/><span class="lab"><font color="Green" title="E58">A10</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c22">x9</font>
 <span class="kw">and </span><br/><a NAME="E11:75_1_1"/><span class="lab"><font color="Green" title="E59">A11</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font>,<font color="Maroon" title="c22">x9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:75"><span class="lab"><font color="Green" title="E49">A1</font></span></a>, <a class="txt" href="#E7:75_1_1"><span class="lab"><font color="Green" title="E56">A8</font></span></a>, <a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c23">x</font> = <font color="Maroon" title="c22">x9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> ;<br/>
<a NAME="E13:75_1_1"/><span class="lab"><font color="Green" title="E60">A12</font></span>: 
<font color="Maroon" title="c20">r9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">s9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:75_1_1"><span class="lab"><font color="Green" title="E56">A8</font></span></a>, <a class="ref" href="aff_1.html#T12" title="AFF_1:th.12">AFF_1:12</a></span>;<br/>
<a NAME="E14:75_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">s9</font>,<font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c22">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:75_1_1"><span class="lab"><font color="Green" title="E59">A11</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E15:75_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c21">s9</font>,<font color="Maroon" title="c20">r9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">s9</font>,<font color="Maroon" title="c22">x9</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="E16:75_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A13</font></span>: 
<font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E17:75_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c15">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/>
<a NAME="E18:75_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c15">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:75_1_1"><span class="lab"><font color="Green" title="E60">A12</font></span></a>, <a class="txt" href="#E5:75_1_1"><span class="lab"><font color="Green" title="E54">A6</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/>
<a NAME="E19:75_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A14</font></span>: 
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c15">s</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/>
<a NAME="E20:75_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c22">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:75_1_1"><span class="lab"><font color="Green" title="E58">A10</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E21:75_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c18">p9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c22">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E22:75_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c19">q9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c19">q9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E23:75_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c13">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/>
<a NAME="E24:75_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A15</font></span>: 
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c13">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:75_1_1"><span class="lab"><font color="Green" title="E57">A9</font></span></a>, <a class="txt" href="#E4:75_1_1"><span class="lab"><font color="Green" title="E53">A5</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E64">A16</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">consider </span><font color="Maroon" title="c24">y9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E2:75_1_1_1"/><span class="lab"><font color="Green" title="E65">A17</font></span>: 
( <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c24">y9</font> &amp; <font color="Maroon" title="c19">q9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">y9</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E3:75_1_1_1"/><span class="lab"><font color="Green" title="E66">A18</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">q</font>
 <span class="kw">and </span><br/><a NAME="E4:75_1_1_1"/><span class="lab"><font color="Green" title="E67">A19</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E5:75_1_1_1"/>
not <font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c24">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:75_1_1_1_1"/>
<font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c24">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:75_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c24">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:75_1_1"><span class="lab"><font color="Green" title="E61">A13</font></span></a>, <a class="txt" href="#E4:75_1_1_1"><span class="lab"><font color="Green" title="E67">A19</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/>
<a NAME="E3:75_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:75_1_1_1"><span class="lab"><font color="Green" title="E65">A17</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/>
<a NAME="E4:75_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/>
<a NAME="E5:75_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:75_1_1"><span class="lab"><font color="Green" title="E60">A12</font></span></a>, <a class="txt" href="#E5:75_1_1"><span class="lab"><font color="Green" title="E54">A6</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:75_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:75_1_1"><span class="lab"><font color="Green" title="E55">A7</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="c25">z9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E7:75_1_1_1"/><span class="lab"><font color="Green" title="E68">A20</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c24">y9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">and </span><br/><a NAME="E8:75_1_1_1"/><span class="lab"><font color="Green" title="E69">A21</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:75"><span class="lab"><font color="Green" title="E49">A1</font></span></a>, <a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c26">z</font> = <font color="Maroon" title="c25">z9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> ;<br/><a NAME="E10:75_1_1_1"/>
<font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c24">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:75_1_1_1"><span class="lab"><font color="Green" title="E68">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="E11:75_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:75_1_1_1"><span class="lab"><font color="Green" title="E65">A17</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/><a NAME="E12:75_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A22</font></span>: 
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/><a NAME="E13:75_1_1_1"/><span class="lab"><font color="Green" title="E71">A23</font></span>: 
<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:75_1_1_1"><span class="lab"><font color="Green" title="E69">A21</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E14:75_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c15">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/><a NAME="E15:75_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:75_1_1"><span class="lab"><font color="Green" title="E62">A14</font></span></a>, <a class="txt" href="#E4:75_1_1_1"><span class="lab"><font color="Green" title="E67">A19</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/><a NAME="E16:75_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:75_1_1"><span class="lab"><font color="Green" title="E63">A15</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/><a NAME="E17:75_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c26">z</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:75_1_1"><span class="lab"><font color="Green" title="E55">A7</font></span></a>, <a class="txt" href="#E12:75_1_1_1"><span class="lab"><font color="Green" title="E70">A22</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/><a NAME="E18:75_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c19">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:75_1_1_1"><span class="lab"><font color="Green" title="E71">A23</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/><a NAME="E19:75_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A24</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font>,<font color="Maroon" title="c19">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E20:75_1_1_1"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font>,<font color="Maroon" title="c22">x9</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c18">p9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:75_1_1"><span class="lab"><font color="Green" title="E58">A10</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></span>;<br/><a NAME="E21:75_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="c22">x9</font>,<font color="Maroon" title="c21">s9</font>,<font color="Maroon" title="c18">p9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:75_1_1_1"><span class="lab"><font color="Green" title="E66">A18</font></span></a>, <a class="txt" href="#E19:75_1_1_1"><span class="lab"><font color="Green" title="E72">A24</font></span></a>, <a class="ref" href="aff_1.html#T20" title="AFF_1:th.20">AFF_1:20</a></span>;<br/><a NAME="E22:75_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c19">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:75_1_1_1"><span class="lab"><font color="Green" title="E72">A24</font></span></a>, <a class="ref" href="aff_1.html#T19" title="AFF_1:th.19">AFF_1:19</a></span>;<br/><a NAME="E23:75_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c19">q9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:75_1_1"><span class="lab"><font color="Green" title="E61">A13</font></span></a>, <a class="txt" href="#E4:75_1_1_1"><span class="lab"><font color="Green" title="E67">A19</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/><span class="kw">hence </span><a NAME="E24:75_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:75_1_1"><span class="lab"><font color="Green" title="E55">A7</font></span></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E26:75_1_1"/>
<font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c22">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:75_1_1"><span class="lab"><font color="Green" title="E59">A11</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="E27:75_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A25</font></span>: 
<font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E28:75_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c14">r</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/>
<a NAME="E29:75_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c14">r</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:75_1_1"><span class="lab"><font color="Green" title="E60">A12</font></span></a>, <a class="txt" href="#E5:75_1_1"><span class="lab"><font color="Green" title="E54">A6</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/>
<a NAME="E30:75_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A26</font></span>: 
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c14">r</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E67">A27</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">consider </span><font color="Maroon" title="c24">y9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E2:75_1_1_2"/><span class="lab"><font color="Green" title="E68">A28</font></span>: 
( <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c24">y9</font> &amp; <font color="Maroon" title="c19">q9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">y9</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E3:75_1_1_2"/><span class="lab"><font color="Green" title="E69">A29</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">q</font>
 <span class="kw">and </span><br/><a NAME="E4:75_1_1_2"/><span class="lab"><font color="Green" title="E70">A30</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">r</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E5:75_1_1_2"/>
not <font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c24">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:75_1_1_2_1"/>
<font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c24">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:75_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c24">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:75_1_1"><span class="lab"><font color="Green" title="E65">A25</font></span></a>, <a class="txt" href="#E4:75_1_1_2"><span class="lab"><font color="Green" title="E70">A30</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/>
<a NAME="E3:75_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:75_1_1_2"><span class="lab"><font color="Green" title="E68">A28</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/>
<a NAME="E4:75_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/>
<a NAME="E5:75_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:75_1_1"><span class="lab"><font color="Green" title="E60">A12</font></span></a>, <a class="txt" href="#E5:75_1_1"><span class="lab"><font color="Green" title="E54">A6</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:75_1_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:75_1_1"><span class="lab"><font color="Green" title="E55">A7</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="c25">z9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E7:75_1_1_2"/><span class="lab"><font color="Green" title="E71">A31</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c24">y9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">and </span><br/><a NAME="E8:75_1_1_2"/><span class="lab"><font color="Green" title="E72">A32</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:75"><span class="lab"><font color="Green" title="E49">A1</font></span></a>, <a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c26">z</font> = <font color="Maroon" title="c25">z9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> ;<br/><a NAME="E10:75_1_1_2"/>
<font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c24">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:75_1_1_2"><span class="lab"><font color="Green" title="E71">A31</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="E11:75_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:75_1_1_2"><span class="lab"><font color="Green" title="E68">A28</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/><a NAME="E12:75_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A33</font></span>: 
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/><a NAME="E13:75_1_1_2"/><span class="lab"><font color="Green" title="E74">A34</font></span>: 
<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:75_1_1_2"><span class="lab"><font color="Green" title="E72">A32</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E14:75_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c14">r</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/><a NAME="E15:75_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:75_1_1"><span class="lab"><font color="Green" title="E66">A26</font></span></a>, <a class="txt" href="#E4:75_1_1_2"><span class="lab"><font color="Green" title="E70">A30</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/><a NAME="E16:75_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:75_1_1"><span class="lab"><font color="Green" title="E63">A15</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/><a NAME="E17:75_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c26">z</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">q</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:75_1_1"><span class="lab"><font color="Green" title="E55">A7</font></span></a>, <a class="txt" href="#E12:75_1_1_2"><span class="lab"><font color="Green" title="E73">A33</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/><a NAME="E18:75_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c19">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:75_1_1_2"><span class="lab"><font color="Green" title="E74">A34</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/><a NAME="E19:75_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A35</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c19">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E20:75_1_1_2"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c22">x9</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c19">q9</font>,<font color="Maroon" title="c18">p9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:75_1_1"><span class="lab"><font color="Green" title="E58">A10</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></span>;<br/><a NAME="E21:75_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c18">p9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:75_1_1_2"><span class="lab"><font color="Green" title="E69">A29</font></span></a>, <a class="txt" href="#E19:75_1_1_2"><span class="lab"><font color="Green" title="E75">A35</font></span></a>, <a class="ref" href="aff_1.html#T20" title="AFF_1:th.20">AFF_1:20</a></span>;<br/><a NAME="E22:75_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c19">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:75_1_1_2"><span class="lab"><font color="Green" title="E75">A35</font></span></a>, <a class="ref" href="aff_1.html#T19" title="AFF_1:th.19">AFF_1:19</a></span>;<br/><a NAME="E23:75_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c19">q9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:75_1_1"><span class="lab"><font color="Green" title="E65">A25</font></span></a>, <a class="txt" href="#E4:75_1_1_2"><span class="lab"><font color="Green" title="E70">A30</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/><span class="kw">hence </span><a NAME="E24:75_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:75_1_1"><span class="lab"><font color="Green" title="E55">A7</font></span></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E32:75_1_1"/>
<font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c19">q9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c22">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:75_1_1"><span class="lab"><font color="Green" title="E58">A10</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="E33:75_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c19">q9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c18">p9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E34:75_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c12">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/>
<a NAME="E35:75_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A36</font></span>: 
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c12">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:75_1_1"><span class="lab"><font color="Green" title="E57">A9</font></span></a>, <a class="txt" href="#E4:75_1_1"><span class="lab"><font color="Green" title="E53">A5</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E69">A37</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1_1_3"><span class="kw">now </span></a><div class="add"><span class="kw">consider </span><font color="Maroon" title="c24">y9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E2:75_1_1_3"/><span class="lab"><font color="Green" title="E70">A38</font></span>: 
( <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c24">y9</font> &amp; <font color="Maroon" title="c18">p9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">y9</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E3:75_1_1_3"/><span class="lab"><font color="Green" title="E71">A39</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">p</font>
 <span class="kw">and </span><br/><a NAME="E4:75_1_1_3"/><span class="lab"><font color="Green" title="E72">A40</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E5:75_1_1_3"/>
not <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c24">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1_1_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:75_1_1_3_1"/>
<font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c24">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:75_1_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c24">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:75_1_1"><span class="lab"><font color="Green" title="E61">A13</font></span></a>, <a class="txt" href="#E4:75_1_1_3"><span class="lab"><font color="Green" title="E72">A40</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/>
<a NAME="E3:75_1_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:75_1_1_3"><span class="lab"><font color="Green" title="E70">A38</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/>
<a NAME="E4:75_1_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/>
<a NAME="E5:75_1_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:75_1_1"><span class="lab"><font color="Green" title="E60">A12</font></span></a>, <a class="txt" href="#E5:75_1_1"><span class="lab"><font color="Green" title="E54">A6</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:75_1_1_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:75_1_1"><span class="lab"><font color="Green" title="E55">A7</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="c25">z9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E7:75_1_1_3"/><span class="lab"><font color="Green" title="E73">A41</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c24">y9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">and </span><br/><a NAME="E8:75_1_1_3"/><span class="lab"><font color="Green" title="E74">A42</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:75"><span class="lab"><font color="Green" title="E49">A1</font></span></a>, <a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c26">z</font> = <font color="Maroon" title="c25">z9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> ;<br/><a NAME="E10:75_1_1_3"/>
<font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c24">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:75_1_1_3"><span class="lab"><font color="Green" title="E73">A41</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="E11:75_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:75_1_1_3"><span class="lab"><font color="Green" title="E70">A38</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/><a NAME="E12:75_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A43</font></span>: 
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/><a NAME="E13:75_1_1_3"/><span class="lab"><font color="Green" title="E76">A44</font></span>: 
<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:75_1_1_3"><span class="lab"><font color="Green" title="E74">A42</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E14:75_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c15">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/><a NAME="E15:75_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:75_1_1"><span class="lab"><font color="Green" title="E62">A14</font></span></a>, <a class="txt" href="#E4:75_1_1_3"><span class="lab"><font color="Green" title="E72">A40</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/><a NAME="E16:75_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:75_1_1"><span class="lab"><font color="Green" title="E68">A36</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/><a NAME="E17:75_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c26">z</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:75_1_1"><span class="lab"><font color="Green" title="E55">A7</font></span></a>, <a class="txt" href="#E12:75_1_1_3"><span class="lab"><font color="Green" title="E75">A43</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/><a NAME="E18:75_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c18">p9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:75_1_1_3"><span class="lab"><font color="Green" title="E76">A44</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/><a NAME="E19:75_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A45</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font>,<font color="Maroon" title="c18">p9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E20:75_1_1_3"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font>,<font color="Maroon" title="c22">x9</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c19">q9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:75_1_1"><span class="lab"><font color="Green" title="E58">A10</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></span>;<br/><a NAME="E21:75_1_1_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font>,<font color="Maroon" title="c19">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:75_1_1_3"><span class="lab"><font color="Green" title="E71">A39</font></span></a>, <a class="txt" href="#E19:75_1_1_3"><span class="lab"><font color="Green" title="E77">A45</font></span></a>, <a class="ref" href="aff_1.html#T20" title="AFF_1:th.20">AFF_1:20</a></span>;<br/><a NAME="E22:75_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c21">s9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c19">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:75_1_1_3"><span class="lab"><font color="Green" title="E77">A45</font></span></a>, <a class="ref" href="aff_1.html#T19" title="AFF_1:th.19">AFF_1:19</a></span>;<br/><a NAME="E23:75_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c19">q9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:75_1_1"><span class="lab"><font color="Green" title="E61">A13</font></span></a>, <a class="txt" href="#E4:75_1_1_3"><span class="lab"><font color="Green" title="E72">A40</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/><span class="kw">hence </span><a NAME="E24:75_1_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:75_1_1"><span class="lab"><font color="Green" title="E55">A7</font></span></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="75_1_1_4"><span class="kw">now </span></a><div class="add"><span class="kw">consider </span><font color="Maroon" title="c24">y9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E2:75_1_1_4"/><span class="lab"><font color="Green" title="E70">A46</font></span>: 
( <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c24">y9</font> &amp; <font color="Maroon" title="c18">p9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">y9</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E3:75_1_1_4"/><span class="lab"><font color="Green" title="E71">A47</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">p</font>
 <span class="kw">and </span><br/><a NAME="E4:75_1_1_4"/><span class="lab"><font color="Green" title="E72">A48</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">r</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E5:75_1_1_4"/>
not <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c24">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1_1_4_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:75_1_1_4_1"/>
<font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c24">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:75_1_1_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c24">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:75_1_1"><span class="lab"><font color="Green" title="E65">A25</font></span></a>, <a class="txt" href="#E4:75_1_1_4"><span class="lab"><font color="Green" title="E72">A48</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/>
<a NAME="E3:75_1_1_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:75_1_1_4"><span class="lab"><font color="Green" title="E70">A46</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/>
<a NAME="E4:75_1_1_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">r</font>,<font color="Maroon" title="c15">s</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/>
<a NAME="E5:75_1_1_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:75_1_1"><span class="lab"><font color="Green" title="E60">A12</font></span></a>, <a class="txt" href="#E5:75_1_1"><span class="lab"><font color="Green" title="E54">A6</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:75_1_1_4_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:75_1_1"><span class="lab"><font color="Green" title="E55">A7</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="c25">z9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E7:75_1_1_4"/><span class="lab"><font color="Green" title="E73">A49</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c24">y9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">and </span><br/><a NAME="E8:75_1_1_4"/><span class="lab"><font color="Green" title="E74">A50</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:75"><span class="lab"><font color="Green" title="E49">A1</font></span></a>, <a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c26">z</font> = <font color="Maroon" title="c25">z9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> ;<br/><a NAME="E10:75_1_1_4"/>
<font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c24">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:75_1_1_4"><span class="lab"><font color="Green" title="E73">A49</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="E11:75_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:75_1_1_4"><span class="lab"><font color="Green" title="E70">A46</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/><a NAME="E12:75_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A51</font></span>: 
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/><a NAME="E13:75_1_1_4"/><span class="lab"><font color="Green" title="E76">A52</font></span>: 
<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c25">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:75_1_1_4"><span class="lab"><font color="Green" title="E74">A50</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E14:75_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c14">r</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/><a NAME="E15:75_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:75_1_1"><span class="lab"><font color="Green" title="E66">A26</font></span></a>, <a class="txt" href="#E4:75_1_1_4"><span class="lab"><font color="Green" title="E72">A48</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/><a NAME="E16:75_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:75_1_1"><span class="lab"><font color="Green" title="E68">A36</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/><a NAME="E17:75_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c26">z</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c26">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:75_1_1"><span class="lab"><font color="Green" title="E55">A7</font></span></a>, <a class="txt" href="#E12:75_1_1_4"><span class="lab"><font color="Green" title="E75">A51</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/><a NAME="E18:75_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c18">p9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:75_1_1_4"><span class="lab"><font color="Green" title="E76">A52</font></span></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/><a NAME="E19:75_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A53</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c18">p9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E20:75_1_1_4"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c22">x9</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c19">q9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:75_1_1"><span class="lab"><font color="Green" title="E58">A10</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></span>;<br/><a NAME="E21:75_1_1_4"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c19">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:75_1_1_4"><span class="lab"><font color="Green" title="E71">A47</font></span></a>, <a class="txt" href="#E19:75_1_1_4"><span class="lab"><font color="Green" title="E77">A53</font></span></a>, <a class="ref" href="aff_1.html#T20" title="AFF_1:th.20">AFF_1:20</a></span>;<br/><a NAME="E22:75_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c20">r9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c19">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:75_1_1_4"><span class="lab"><font color="Green" title="E77">A53</font></span></a>, <a class="ref" href="aff_1.html#T19" title="AFF_1:th.19">AFF_1:19</a></span>;<br/><a NAME="E23:75_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c18">p9</font>,<font color="Maroon" title="c19">q9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">r9</font>,<font color="Maroon" title="c21">s9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:75_1_1"><span class="lab"><font color="Green" title="E65">A25</font></span></a>, <a class="txt" href="#E4:75_1_1_4"><span class="lab"><font color="Green" title="E72">A48</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/><span class="kw">hence </span><a NAME="E24:75_1_1_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:75_1_1"><span class="lab"><font color="Green" title="E55">A7</font></span></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E38:75_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:75_1_1"><span class="lab"><font color="Green" title="E56">A8</font></span></a>, <a class="txt" href="#E36:75_1_1"><span class="lab"><font color="Green" title="E69">A37</font></span></a>, <a class="txt" href="#E31:75_1_1"><span class="lab"><font color="Green" title="E67">A27</font></span></a>, <a class="txt" href="#E25:75_1_1"><span class="lab"><font color="Green" title="E64">A16</font></span></a>, <a class="ref" href="aff_1.html#T12" title="AFF_1:th.12">AFF_1:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<a NAME="E3:75"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font>  ex <font color="Olive" title="b4">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">x</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">x</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:75"/>
<font color="Maroon" title="c7">POS</font> is   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:75"><span class="lab"><font color="Green" title="E49">A1</font></span></a>, <a class="txt" href="#E2:75"><span class="lab"><font color="Green" title="E50">A2</font></span></a>, <a class="ref" href="analmetr.html#D10" target="_self" title="ANALMETR:def.10">Def10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
