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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> 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> holds <br/><font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">a</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> 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> holds <br/><font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</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> 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> implies <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c9">a</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font> )</span><br/>







<b>assume </b><a NAME="E1:79"/>
<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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c9">a</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font></span><br/>

<b>then consider </b><font color="Maroon" title="c11">p</font>, <font color="Maroon" title="c12">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="E3:79"/><i><font color="Green" title="E61">A1</font></i>: 
( <font color="Maroon" title="c11">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">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="c11">p</font>,<font color="Maroon" title="c12">q</font> )
 <b>and </b><br/><a NAME="E4:79"/><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="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c12">q</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D14" target="_self" title="ANALMETR:def.14">Def14</a></i>;<br/>
<a NAME="E5:79"/>
<font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c12">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font>
 
<b>by </b><i><a class="txt" href="#E4:79"><i><font color="Green" title="E62">A2</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>
<a NAME="E6:79"/><b>then </b>
<font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c12">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c9">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>
<a NAME="E7:79"/><b>then </b>
<font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c9">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c12">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="E8:79"/>
<font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c9">a</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="#E3:79"><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>; <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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