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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>, <font color="Olive" title="b2">M</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="b3">r</font>, <font color="Olive" title="b4">s</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="b3">r</font>,<font color="Olive" title="b4">s</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Olive" title="b1">K</font> &amp; <font color="Olive" title="b1">K</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Olive" title="b2">M</font> holds <br/><font color="Olive" title="b3">r</font>,<font color="Olive" title="b4">s</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Olive" title="b2">M</font></span><br/><b>let </b><font color="Maroon" title="c8">K</font>, <font color="Maroon" title="c9">M</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">r</font>, <font color="Olive" title="b2">s</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">r</font>,<font color="Olive" title="b2">s</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font> &amp; <font color="Maroon" title="c8">K</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font> holds <br/><font color="Olive" title="b1">r</font>,<font color="Olive" title="b2">s</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c9">M</font></span><br/><b>let </b><font color="Maroon" title="c10">r</font>, <font color="Maroon" title="c11">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c10">r</font>,<font color="Maroon" title="c11">s</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font> &amp; <font color="Maroon" title="c8">K</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font> implies <font color="Maroon" title="c10">r</font>,<font color="Maroon" title="c11">s</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c9">M</font> )</span><br/>









<b>assume </b><b>that </b><br/><a NAME="E1:82"/><i><font color="Green" title="E62">A1</font></i>: 
<font color="Maroon" title="c10">r</font>,<font color="Maroon" title="c11">s</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font>
 <b>and </b><br/><a NAME="E2:82"/><i><font color="Green" title="E63">A2</font></i>: 
<font color="Maroon" title="c8">K</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">r</font>,<font color="Maroon" title="c11">s</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c9">M</font></span><br/>

<b>consider </b><font color="Maroon" title="c12">p</font>, <font color="Maroon" title="c13">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="E4:82"/><i><font color="Green" title="E64">A3</font></i>: 
( <font color="Maroon" title="c12">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">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="c12">p</font>,<font color="Maroon" title="c13">q</font> &amp; <font color="Maroon" title="c10">r</font>,<font color="Maroon" title="c11">s</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> )
 <b>by </b><i><a class="txt" href="analmetr.html#E1:82"><i><font color="Green" title="E62">A1</font></i></a>, <a class="ref" href="analmetr.html#D14" target="_self" title="ANALMETR:def.14">Def14</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c14">a</font>, <font color="Maroon" title="c15">b</font>, <font color="Maroon" title="c16">c</font>, <font color="Maroon" title="c17">d</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="E6:82"/><i><font color="Green" title="E65">A4</font></i>: 
( <font color="Maroon" title="c14">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">b</font> &amp; <font color="Maroon" title="c16">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">d</font> )
 <b>and </b><br/><a NAME="E7:82"/><i><font color="Green" title="E66">A5</font></i>: 
<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="c14">a</font>,<font color="Maroon" title="c15">b</font>
 <b>and </b><br/><a NAME="E8:82"/><i><font color="Green" title="E67">A6</font></i>: 
( <font color="Maroon" title="c9">M</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="c16">c</font>,<font color="Maroon" title="c17">d</font> &amp; <font color="Maroon" title="c14">a</font>,<font color="Maroon" title="c15">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">c</font>,<font color="Maroon" title="c17">d</font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E2:82"><i><font color="Green" title="E63">A2</font></i></a>, <a class="ref" href="analmetr.html#D16" target="_self" title="ANALMETR:def.16">Def16</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c18">p'</font> = <font color="Maroon" title="c12">p</font>, <font color="Maroon" title="c19">q'</font> = <font color="Maroon" title="c13">q</font>, <font color="Maroon" title="c20">a'</font> = <font color="Maroon" title="c14">a</font>, <font color="Maroon" title="c21">b'</font> = <font color="Maroon" title="c15">b</font>, <font color="Maroon" title="c22">c'</font> = <font color="Maroon" title="c16">c</font>, <font color="Maroon" title="c23">d'</font> = <font color="Maroon" title="c17">d</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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="E10:82"/><i><font color="Green" title="E68">A7</font></i>: 
( <font color="Maroon" title="c8">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c20">a'</font>,<font color="Maroon" title="c21">b'</font> &amp; <font color="Maroon" title="c8">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E4:82"><i><font color="Green" title="E64">A3</font></i></a>, <a class="txt" href="analmetr.html#E7:82"><i><font color="Green" title="E66">A5</font></i></a>, <a class="ref" href="analmetr.html#T56" target="_self" title="ANALMETR:th.56">Th56</a></i>;<br/>
<a NAME="E11:82"/><b>then </b>
( <font color="Maroon" title="c18">p'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">K</font> &amp; <font color="Maroon" title="c19">q'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">K</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a></i>;<br/>
<a NAME="E12:82"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">a'</font>,<font color="Maroon" title="c21">b'</font>,<font color="Maroon" title="c18">p'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">a'</font>,<font color="Maroon" title="c21">b'</font>,<font color="Maroon" title="c19">q'</font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E10:82"><i><font color="Green" title="E68">A7</font></i></a>, <a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</a></i>;<br/>
<a NAME="E13:82"/><b>then </b><i><font color="Green" title="E69">A8</font></i>: 
<font color="Maroon" title="c20">a'</font>,<font color="Maroon" title="c21">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T19" title="AFF_1:th.19">AFF_1:19</a></i>;<br/>
<a NAME="E14:82"/>
<font color="Maroon" title="c20">a'</font>,<font color="Maroon" title="c21">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">c'</font>,<font color="Maroon" title="c23">d'</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E8:82"><i><font color="Green" title="E67">A6</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/>
<a NAME="E15:82"/><b>then </b>
<font color="Maroon" title="c18">p'</font>,<font color="Maroon" title="c19">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">c'</font>,<font color="Maroon" title="c23">d'</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E6:82"><i><font color="Green" title="E65">A4</font></i></a>, <a class="txt" href="analmetr.html#E13:82"><i><font color="Green" title="E69">A8</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E16:82"/><b>then </b><i><font color="Green" title="E70">A9</font></i>: 
<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="c16">c</font>,<font color="Maroon" title="c17">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="E17:82"/>
<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="c10">r</font>,<font color="Maroon" title="c11">s</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E4:82"><i><font color="Green" title="E64">A3</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>
<a NAME="E18:82"/><b>then </b>
<font color="Maroon" title="c10">r</font>,<font color="Maroon" title="c11">s</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c16">c</font>,<font color="Maroon" title="c17">d</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E4:82"><i><font color="Green" title="E64">A3</font></i></a>, <a class="txt" href="analmetr.html#E16:82"><i><font color="Green" title="E70">A9</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>
<b>hence </b><a NAME="E19:82"/>
<font color="Maroon" title="c10">r</font>,<font color="Maroon" title="c11">s</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c9">M</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E6:82"><i><font color="Green" title="E65">A4</font></i></a>, <a class="txt" href="analmetr.html#E8:82"><i><font color="Green" title="E67">A6</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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