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<b>let </b><font color="Maroon" title="c1">MS</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">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="c1">MS</font><br/> for <font color="Olive" title="b3">A</font>, <font color="Olive" title="b4">K</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">MS</font>  st <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> &amp; ( <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="Olive" title="b4">K</font> or <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="Olive" title="b4">K</font> ) &amp; <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="Olive" title="b3">A</font> holds <br/><font color="Olive" title="b4">K</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Olive" title="b3">A</font></span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">MS</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">K</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">MS</font>  st <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> &amp; ( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Olive" title="b2">K</font> or <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Olive" title="b2">K</font> ) &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Olive" title="b1">A</font> holds <br/><font color="Olive" title="b2">K</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Olive" title="b1">A</font></span><br/><b>let </b><font color="Maroon" title="c4">A</font>, <font color="Maroon" title="c5">K</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">MS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> &amp; ( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c5">K</font> or <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c5">K</font> ) &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c4">A</font> implies <font color="Maroon" title="c5">K</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c4">A</font> )</span><br/>





<b>assume </b><b>that </b><br/><a NAME="E1:10"/><i><font color="Green" title="E10">A1</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font>
 <b>and </b><br/><a NAME="E2:10"/><i><font color="Green" title="E11">A2</font></i>: 
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c5">K</font> or <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c5">K</font> )
 <b>and </b><br/><a NAME="E3:10"/><i><font color="Green" title="E12">A3</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c4">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">K</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c4">A</font></span><br/>

<a NAME="E4:10"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c5">K</font>
 
<b>by </b><i><a class="txt" href="euclmetr.html#E2:10"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="analmetr.html#T67" title="ANALMETR:th.67">ANALMETR:67</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c6">p</font>, <font color="Maroon" title="c7">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">MS</font><b> such that </b><br/><a NAME="E6:10"/><i><font color="Green" title="E13">A4</font></i>: 
( <font color="Maroon" title="c6">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">q</font> &amp; <font color="Maroon" title="c5">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="c6">p</font>,<font color="Maroon" title="c7">q</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D14" title="ANALMETR:def.14">ANALMETR:def 14</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">r</font>, <font color="Maroon" title="c9">s</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">MS</font><b> such that </b><br/><a NAME="E8:10"/><i><font color="Green" title="E14">A5</font></i>: 
( <font color="Maroon" title="c8">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">s</font> &amp; <font color="Maroon" title="c4">A</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="c8">r</font>,<font color="Maroon" title="c9">s</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c9">s</font> )
 <b>by </b><i><a class="txt" href="euclmetr.html#E3:10"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="analmetr.html#D14" title="ANALMETR:def.14">ANALMETR:def 14</a></i>;<br/>
<a NAME="E9:10"/>
<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c9">s</font>
 
<b>by </b><i><a class="txt" href="euclmetr.html#E1:10"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="euclmetr.html#E6:10"><i><font color="Green" title="E13">A4</font></i></a>, <a class="txt" href="euclmetr.html#E8:10"><i><font color="Green" title="E14">A5</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<b>hence </b><a NAME="E10:10"/>
<font color="Maroon" title="c5">K</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c4">A</font>
 <b>by </b><i><a class="txt" href="euclmetr.html#E6:10"><i><font color="Green" title="E13">A4</font></i></a>, <a class="txt" href="euclmetr.html#E8:10"><i><font color="Green" title="E14">A5</font></i></a>, <a class="ref" href="analmetr.html#D16" title="ANALMETR:def.16">ANALMETR:def 16</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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