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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</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="b5">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>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Olive" title="b5">K</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Olive" title="b5">K</font> holds <br/>( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">d</font>,<font color="Olive" title="b3">c</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">d</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">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>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Olive" title="b1">K</font> holds <br/>( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <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="c6">K</font> &amp; <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c6">K</font> implies ( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font> ) )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:9"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
<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="c6">K</font>
 <span class="kw">and </span><br/><a NAME="E2:9"/><span class="lab"><font color="Green" title="E11">A2</font></span>: 
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c6">K</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="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">K9</font> = <font color="Maroon" title="c6">K</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="c1">MS</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></span>;<br/>
<a NAME="E4:9"/>
<font color="Maroon" title="c6">K</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="#E1:9"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E5:9"/><span class="kw">then </span>
<font color="Maroon" title="c7">K9</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" title="ANALMETR:th.58">ANALMETR:58</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">p9</font>, <font color="Maroon" title="c9">q9</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="c1">MS</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E7:9"/><span class="lab"><font color="Green" title="E12">A3</font></span>: 
( <font color="Maroon" title="c8">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">K9</font> &amp; <font color="Maroon" title="c9">q9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">K9</font> )
 <span class="kw">and </span><br/><a NAME="E8:9"/><span class="lab"><font color="Green" title="E13">A4</font></span>: 
<font color="Maroon" title="c8">p9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T31" title="AFF_1:th.31">AFF_1:31</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">p</font> = <font color="Maroon" title="c8">p9</font>, <font color="Maroon" title="c11">q</font> = <font color="Maroon" title="c9">q9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">MS</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/>
<a NAME="E10:9"/>
( <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="c10">p</font>,<font color="Maroon" title="c11">q</font> &amp; <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">p</font>,<font color="Maroon" title="c11">q</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E2:9"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="txt" href="#E7:9"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="analmetr.html#T75" title="ANALMETR:th.75">ANALMETR:75</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:9"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:9"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>; <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="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><br/>

<span class="kw">hence </span><a NAME="E12:9"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</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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