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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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:81"/><span class="lab"><font color="Green" title="E55">A1</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E2:81"/><span class="lab"><font color="Green" title="E56">A2</font></span>: 
<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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E4:81"/><span class="lab"><font color="Green" title="E57">A3</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E5:81"/><span class="lab"><font color="Green" title="E58">A4</font></span>: 
<font color="Maroon" title="c8">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">q</font>)
 <span class="kw">and </span><br/><a NAME="E6:81"/><span class="lab"><font color="Green" title="E59">A5</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:81"><span class="lab"><font color="Green" title="E55">A1</font></span></a></span>;<br/>
<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E8:81"/><span class="lab"><font color="Green" title="E60">A6</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E9:81"/><span class="lab"><font color="Green" title="E61">A7</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E10:81"/><span class="lab"><font color="Green" title="E62">A8</font></span>: 
<font color="Maroon" title="c8">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Maroon" title="c14">a</font>,<font color="Maroon" title="c15">b</font>)
 <span class="kw">and </span><br/><a NAME="E11:81"/><span class="lab"><font color="Green" title="E63">A9</font></span>: 
<font color="Maroon" title="c9">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Maroon" title="c16">c</font>,<font color="Maroon" title="c17">d</font>)
 <span class="kw">and </span><br/><a NAME="E12:81"/><span class="lab"><font color="Green" title="E64">A10</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:81"><span class="lab"><font color="Green" title="E56">A2</font></span></a></span>;<br/>
<span class="kw">reconsider </span><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">a9</font> = <font color="Maroon" title="c14">a</font>, <font color="Maroon" title="c21">b9</font> = <font color="Maroon" title="c15">b</font>, <font color="Maroon" title="c22">c9</font> = <font color="Maroon" title="c16">c</font>, <font color="Maroon" title="c23">d9</font> = <font color="Maroon" title="c17">d</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="analoaf.html#G1" title="ANALOAF:aggr.1">AffinStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) ;<br/>
<a NAME="E14:81"/><span class="lab"><font color="Green" title="E65">A11</font></span>: 
<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">a9</font>,<font color="Maroon" title="c21">b9</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:81"><span class="lab"><font color="Green" title="E62">A8</font></span></a>, <a class="ref" href="analmetr.html#T41" target="_self" onmouseover="rs('analmetr/T41')" onmouseout="rh()">Th41</a></span>;<br/>
<a NAME="E15:81"/><span class="lab"><font color="Green" title="E66">A12</font></span>: 
<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">p9</font>,<font color="Maroon" title="c19">q9</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:81"><span class="lab"><font color="Green" title="E58">A4</font></span></a>, <a class="ref" href="analmetr.html#T41" target="_self" onmouseover="rs('analmetr/T41')" onmouseout="rh()">Th41</a></span>;<br/>
<a NAME="E16:81"/><span class="kw">then </span>
<font color="Maroon" title="c19">q9</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" onmouseover="rs('aff_1/T15')" onmouseout="rh()">AFF_1:15</a></span>;<br/>
<a NAME="E17:81"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A13</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">a9</font>,<font color="Maroon" title="c21">b9</font>,<font color="Maroon" title="c19">q9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:81"><span class="lab"><font color="Green" title="E65">A11</font></span></a>, <a class="ref" href="aff_1.html#D2" onmouseover="rs('aff_1/D2')" onmouseout="rh()">AFF_1:def 2</a></span>;<br/>
<a NAME="E18:81"/>
<font color="Maroon" title="c18">p9</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:81"><span class="lab"><font color="Green" title="E66">A12</font></span></a>, <a class="ref" href="aff_1.html#T15" onmouseover="rs('aff_1/T15')" onmouseout="rh()">AFF_1:15</a></span>;<br/>
<a NAME="E19:81"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">a9</font>,<font color="Maroon" title="c21">b9</font>,<font color="Maroon" title="c18">p9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:81"><span class="lab"><font color="Green" title="E65">A11</font></span></a>, <a class="ref" href="aff_1.html#D2" onmouseover="rs('aff_1/D2')" onmouseout="rh()">AFF_1:def 2</a></span>;<br/>
<a NAME="E20:81"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A14</font></span>: 
<font color="Maroon" title="c20">a9</font>,<font color="Maroon" title="c21">b9</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="#E17:81"><span class="lab"><font color="Green" title="E67">A13</font></span></a>, <a class="ref" href="aff_1.html#T10" onmouseover="rs('aff_1/T10')" onmouseout="rh()">AFF_1:10</a></span>;<br/>
<a NAME="E21:81"/><span class="lab"><font color="Green" title="E69">A15</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="c10">r</font>,<font color="Maroon" title="c11">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:81"><span class="lab"><font color="Green" title="E59">A5</font></span></a>, <a class="ref" href="analmetr.html#D8" target="_self" onmouseover="rs('analmetr/D8')" onmouseout="rh()">Def7</a></span>;<br/>
<a NAME="E22:81"/>
<font color="Maroon" title="c20">a9</font>,<font color="Maroon" title="c21">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">c9</font>,<font color="Maroon" title="c23">d9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:81"><span class="lab"><font color="Green" title="E64">A10</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/>
<a NAME="E23:81"/><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">c9</font>,<font color="Maroon" title="c23">d9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:81"><span class="lab"><font color="Green" title="E60">A6</font></span></a>, <a class="txt" href="#E20:81"><span class="lab"><font color="Green" title="E68">A14</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E24:81"/><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="c16">c</font>,<font color="Maroon" title="c17">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/>
<a NAME="E25:81"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:81"><span class="lab"><font color="Green" title="E57">A3</font></span></a>, <a class="txt" href="#E21:81"><span class="lab"><font color="Green" title="E69">A15</font></span></a>, <a class="ref" href="analmetr.html#D8" target="_self" onmouseover="rs('analmetr/D8')" onmouseout="rh()">Def7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E26:81"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E9:81"><span class="lab"><font color="Green" title="E61">A7</font></span></a>, <a class="txt" href="#E11:81"><span class="lab"><font color="Green" title="E63">A9</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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