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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">M</font>, <font color="Olive" title="b2">N</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c7">POS</font>  st <font color="Olive" title="b1">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Olive" title="b2">N</font> holds <br/> ex <font color="Olive" title="b3">p</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="b3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> )</span><br/><b>let </b><font color="Maroon" title="c8">M</font>, <font color="Maroon" title="c9">N</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"> ( <font color="Maroon" title="c8">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c9">N</font> implies  ex <font color="Olive" title="b1">p</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">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">N</font> ) )</span><br/>





<b>assume </b><a NAME="E1:98"/><i><font color="Green" title="E72">A1</font></i>: 
<font color="Maroon" title="c8">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c9">N</font>
 ; <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">p</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">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">N</font> )</span><br/>

<a NAME="E2:98"/><b>then </b><i><font color="Green" title="E73">A2</font></i>: 
not <font color="Maroon" title="c8">M</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">N</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T73" target="_self" title="ANALMETR:th.73">Th73</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">M'</font> = <font color="Maroon" title="c8">M</font>, <font color="Maroon" title="c11">N'</font> = <font color="Maroon" title="c9">N</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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="E4:98"/>
( <font color="Maroon" title="c8">M</font> is <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> &amp; <font color="Maroon" title="c9">N</font> is <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> )
 
<b>by </b><i><a class="txt" href="#E1:98"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="analmetr.html#T62" target="_self" title="ANALMETR:th.62">Th62</a></i>;<br/>
<a NAME="E5:98"/><b>then </b><i><font color="Green" title="E74">A3</font></i>: 
( <font color="Maroon" title="c10">M'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c11">N'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T58" target="_self" title="ANALMETR:th.58">Th58</a></i>;<br/>
<a NAME="E6:98"/>
not <font color="Maroon" title="c10">M'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c11">N'</font>
 
<b>by </b><i><a class="txt" href="#E2:98"><i><font color="Green" title="E73">A2</font></i></a>, <a class="ref" href="analmetr.html#T64" target="_self" title="ANALMETR:th.64">Th64</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c12">p'</font> being   <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><b> such that </b><br/><a NAME="E8:98"/><i><font color="Green" title="E75">A4</font></i>: 
( <font color="Maroon" title="c12">p'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M'</font> &amp; <font color="Maroon" title="c12">p'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N'</font> )
 <b>by </b><i><a class="txt" href="#E5:98"><i><font color="Green" title="E74">A3</font></i></a>, <a class="ref" href="aff_1.html#T72" title="AFF_1:th.72">AFF_1:72</a></i>;<br/>
<b>thus </b><a NAME="E9:98"/>
 ex <font color="Olive" title="b1">p</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">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">N</font> )
 <b>by </b><i><a class="txt" href="#E8:98"><i><font color="Green" title="E75">A4</font></i></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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