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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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b3">p</font> <a href="tarski.html#R2" title="TARSKI: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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <font color="Olive" title="b1">p</font> <a href="tarski.html#R2" title="TARSKI: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 <a href="analoaf.html#G1" title="ANALOAF:aggr.1">AffinStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) ;<br/>
<span class="kw">assume </span><a NAME="E2:98"/><span class="lab"><font color="Green" title="E65">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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <font color="Olive" title="b1">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">N</font> )</span><br/>

<a NAME="E3:98"/><span class="kw">then </span>
<font color="Maroon" title="c8">M</font> is  <a href="analmetr.html#V5" title="ANALMETR:attr.5">being_line</a> 
 
;<br/>
<a NAME="E4:98"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">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#T43" target="_self" onmouseover="rs('analmetr/T43')" onmouseout="rh()">Th43</a></span>;<br/>
<a NAME="E5:98"/>
<font color="Maroon" title="c9">N</font> is  <a href="analmetr.html#V5" title="ANALMETR:attr.5">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:98"><span class="lab"><font color="Green" title="E65">A1</font></span></a>, <a class="ref" href="analmetr.html#T44" target="_self" onmouseover="rs('analmetr/T44')" onmouseout="rh()">Th44</a></span>;<br/>
<a NAME="E6:98"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">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#T43" target="_self" onmouseover="rs('analmetr/T43')" onmouseout="rh()">Th43</a></span>;<br/>
<a NAME="E7:98"/>
 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="#E2:98"><span class="lab"><font color="Green" title="E65">A1</font></span></a>, <a class="ref" href="analmetr.html#T52" target="_self" onmouseover="rs('analmetr/T52')" onmouseout="rh()">Th52</a></span>;<br/>
<a NAME="E8:98"/><span class="kw">then </span>
 not <font color="Maroon" title="c10">M9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c11">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" target="_self" onmouseover="rs('analmetr/T46')" onmouseout="rh()">Th46</a></span>;<br/>
<span class="kw">hence </span><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="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <font color="Olive" title="b1">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">N</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:98"><span class="lab"><font color="Green" title="E66">A2</font></span></a>, <a class="txt" href="#E6:98"><span class="lab"><font color="Green" title="E67">A3</font></span></a>, <a class="ref" href="aff_1.html#T58" onmouseover="rs('aff_1/T58')" onmouseout="rh()">AFF_1:58</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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