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<span class="kw">let </span><font color="Maroon" title="c10">K</font>, <font color="Maroon" title="c11">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">K</font> <a href="analmetr.html#R8" title="ANALMETR:pred.8">//</a> <font color="Maroon" title="c11">M</font> implies <font color="Maroon" title="c11">M</font> <a href="analmetr.html#R8" title="ANALMETR:pred.8">//</a> <font color="Maroon" title="c10">K</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:98_1_1"/>
<font color="Maroon" title="c10">K</font> <a href="analmetr.html#R8" title="ANALMETR:pred.8">//</a> <font color="Maroon" title="c11">M</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c11">M</font> <a href="analmetr.html#R8" title="ANALMETR:pred.8">//</a> <font color="Maroon" title="c10">K</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">a</font>, <font color="Maroon" title="c13">b</font>, <font color="Maroon" title="c14">c</font>, <font color="Maroon" title="c15">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="E3:98_1_1"/><span class="lab"><font color="Green" title="E61">A1</font></span>: 
( <font color="Maroon" title="c12">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">b</font> &amp; <font color="Maroon" title="c14">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">d</font> &amp; <font color="Maroon" title="c10">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">a</font>,<font color="Maroon" title="c13">b</font> &amp; <font color="Maroon" title="c11">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="c14">c</font>,<font color="Maroon" title="c15">d</font> )
 <span class="kw">and </span><br/><a NAME="E4:98_1_1"/><span class="lab"><font color="Green" title="E62">A2</font></span>: 
<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c15">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D16" target="_self" title="ANALMETR:def.16">Def16</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c16">a9</font> = <font color="Maroon" title="c12">a</font>, <font color="Maroon" title="c17">b9</font> = <font color="Maroon" title="c13">b</font>, <font color="Maroon" title="c18">c9</font> = <font color="Maroon" title="c14">c</font>, <font color="Maroon" title="c19">d9</font> = <font color="Maroon" title="c15">d</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="E6:98_1_1"/>
<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c9</font>,<font color="Maroon" title="c19">d9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:98_1_1"><span class="lab"><font color="Green" title="E62">A2</font></span></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/>
<a NAME="E7:98_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c18">c9</font>,<font color="Maroon" title="c19">d9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E8:98_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c15">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:98_1_1"/>
<font color="Maroon" title="c11">M</font> <a href="analmetr.html#R8" title="ANALMETR:pred.8">//</a> <font color="Maroon" title="c10">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:98_1_1"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="analmetr.html#D16" target="_self" title="ANALMETR:def.16">Def16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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