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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">K</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c7">POS</font><br/> for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font>  st <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Olive" title="b1">K</font> &amp; ( <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d</font> or <font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> ) &amp; <font color="Olive" title="b2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b</font> holds <br/><font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Olive" title="b1">K</font></span><br/><b>let </b><font color="Maroon" title="c8">K</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c7">POS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font> &amp; ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> or <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> ) &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> holds <br/><font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font></span><br/><b>let </b><font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c10">b</font>, <font color="Maroon" title="c11">c</font>, <font color="Maroon" title="c12">d</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font> &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> or <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> ) &amp; <font color="Maroon" title="c9">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b</font> implies <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font> )</span><br/>











<b>assume </b><b>that </b><br/><a NAME="E1:79"/><i><font color="Green" title="E61">A1</font></i>: 
<font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font>
 <b>and </b><br/><a NAME="E2:79"/><i><font color="Green" title="E62">A2</font></i>: 
( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> or <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> )
 <b>and </b><br/><a NAME="E3:79"/><i><font color="Green" title="E63">A3</font></i>: 
<font color="Maroon" title="c9">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font></span><br/>

<b>consider </b><font color="Maroon" title="c13">p</font>, <font color="Maroon" title="c14">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font><b> such that </b><br/><a NAME="E5:79"/><i><font color="Green" title="E64">A4</font></i>: 
( <font color="Maroon" title="c13">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c8">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> )
 <b>and </b><br/><a NAME="E6:79"/><i><font color="Green" title="E65">A5</font></i>: 
<font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E1:79"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="analmetr.html#D14" target="_self" title="ANALMETR:def.14">Def14</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c15">a'</font> = <font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c16">b'</font> = <font color="Maroon" title="c10">b</font>, <font color="Maroon" title="c17">c'</font> = <font color="Maroon" title="c11">c</font>, <font color="Maroon" title="c18">d'</font> = <font color="Maroon" title="c12">d</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/>
<a NAME="E8:79"/>
( <font color="Maroon" title="c15">a'</font>,<font color="Maroon" title="c16">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c18">d'</font> or <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c18">d'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">a'</font>,<font color="Maroon" title="c16">b'</font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E2:79"><i><font color="Green" title="E62">A2</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/>
<a NAME="E9:79"/><b>then </b>
<font color="Maroon" title="c15">a'</font>,<font color="Maroon" title="c16">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c18">d'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E10:79"/><b>then </b>
<font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/>
<a NAME="E11:79"/><b>then </b>
<font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E3:79"><i><font color="Green" title="E63">A3</font></i></a>, <a class="txt" href="analmetr.html#E6:79"><i><font color="Green" title="E65">A5</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>
<a NAME="E12:79"/><b>then </b>
<font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>
<b>hence </b><a NAME="E13:79"/>
<font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E5:79"><i><font color="Green" title="E64">A4</font></i></a>, <a class="ref" href="analmetr.html#D14" target="_self" title="ANALMETR:def.14">Def14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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