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<b>let </b><font color="Maroon" title="c7">POS</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</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> 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">K</font> is <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> holds <br/> ex <font color="Olive" title="b3">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="b2">a</font>,<font color="Olive" title="b3">x</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Olive" title="b1">K</font> &amp; <font color="Olive" title="b3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> 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="Maroon" title="c8">K</font> is <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> holds <br/> ex <font color="Olive" title="b2">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">x</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font> &amp; <font color="Olive" title="b2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">K</font> )</span><br/><b>let </b><font color="Maroon" title="c9">a</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="c8">K</font> is <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> implies  ex <font color="Olive" title="b1">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="Maroon" title="c9">a</font>,<font color="Olive" title="b1">x</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">K</font> ) )</span><br/>





<b>assume </b><a NAME="E1:102"/>
<font color="Maroon" title="c8">K</font> is <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">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="Maroon" title="c9">a</font>,<font color="Olive" title="b1">x</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">K</font> )</span><br/>

<b>then consider </b><font color="Maroon" title="c10">p</font>, <font color="Maroon" title="c11">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="E3:102"/><i><font color="Green" title="E74">A1</font></i>: 
( <font color="Maroon" title="c10">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">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="c10">p</font>,<font color="Maroon" title="c11">q</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D13" target="_self" title="ANALMETR:def.13">Def13</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c12">x</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="E5:102"/><i><font color="Green" title="E75">A2</font></i>: 
<font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c12">x</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">p</font>,<font color="Maroon" title="c11">q</font>
 <b>and </b><br/><a NAME="E6:102"/><i><font color="Green" title="E76">A3</font></i>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">p</font>,<font color="Maroon" title="c11">q</font>,<font color="Maroon" title="c12">x</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T91" target="_self" title="ANALMETR:th.91">Th91</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c12">x</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="c12">x</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font> &amp; <font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">K</font> )</span><br/>

<b>thus </b><a NAME="E7:102"/>
<font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c12">x</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="#E3:102"><i><font color="Green" title="E74">A1</font></i></a>, <a class="txt" href="#E5:102"><i><font color="Green" title="E75">A2</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"> <font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">K</font></span><br/>

<b>thus </b><a NAME="E8:102"/>
<font color="Maroon" title="c12">x</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="txt" href="#E3:102"><i><font color="Green" title="E74">A1</font></i></a>, <a class="txt" href="#E6:102"><i><font color="Green" title="E76">A3</font></i></a>, <a class="ref" href="analmetr.html#D12" target="_self" title="ANALMETR:def.12">Def12</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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