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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>





<span class="kw">reconsider </span><font color="Maroon" title="c10">M9</font> = <font color="Maroon" title="c8">M</font>, <font color="Maroon" title="c11">N9</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/>
<span class="kw">assume </span><a NAME="E2:120"/><span class="lab"><font color="Green" title="E72">A1</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E3:120"/><span class="kw">then </span>
<font color="Maroon" title="c8">M</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T62" target="_self" title="ANALMETR:th.62">Th62</a></span>;<br/>
<a NAME="E4:120"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A2</font></span>: 
<font color="Maroon" title="c10">M9</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T58" target="_self" title="ANALMETR:th.58">Th58</a></span>;<br/>
<a NAME="E5:120"/>
<font color="Maroon" title="c9">N</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:120"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="analmetr.html#T62" target="_self" title="ANALMETR:th.62">Th62</a></span>;<br/>
<a NAME="E6:120"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A3</font></span>: 
<font color="Maroon" title="c11">N9</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T58" target="_self" title="ANALMETR:th.58">Th58</a></span>;<br/>
<a NAME="E7:120"/>
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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:120"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="analmetr.html#T73" target="_self" title="ANALMETR:th.73">Th73</a></span>;<br/>
<a NAME="E8:120"/><span class="kw">then </span>
not <font color="Maroon" title="c10">M9</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c11">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T64" target="_self" title="ANALMETR:th.64">Th64</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:120"/>
 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 class="kw">by</span> <span class="lab"><a class="txt" href="#E4:120"><span class="lab"><font color="Green" title="E73">A2</font></span></a>, <a class="txt" href="#E6:120"><span class="lab"><font color="Green" title="E74">A3</font></span></a>, <a class="ref" href="aff_1.html#T72" title="AFF_1:th.72">AFF_1:72</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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