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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">K</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c7">POS</font><br/> for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font>  st <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Olive" title="b1">K</font> holds <br/> ex <font color="Olive" title="b4">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/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">p</font> &amp; <font color="Olive" title="b4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c8">K</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"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</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="Maroon" title="c8">K</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/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">p</font> &amp; <font color="Olive" title="b3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">K</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c10">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</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/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">p</font> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">K</font> ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:122"/>
<font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</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/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">p</font> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">K</font> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">p</font>, <font color="Maroon" title="c12">q</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="E3:122"/>
<font color="Maroon" title="c11">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">q</font>
 <span class="kw">and </span><br/><a NAME="E4:122"/><span class="lab"><font color="Green" title="E73">A1</font></span>: 
<font color="Maroon" title="c8">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="c11">p</font>,<font color="Maroon" title="c12">q</font>
 <span class="kw">and </span><br/><a NAME="E5:122"/><span class="lab"><font color="Green" title="E74">A2</font></span>: 
<font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c12">q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D14" target="_self" title="ANALMETR:def.14">Def14</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c13">c</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="E7:122"/><span class="lab"><font color="Green" title="E75">A3</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c13">c</font>
 <span class="kw">and </span><br/><a NAME="E8:122"/><span class="lab"><font color="Green" title="E76">A4</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c12">q</font>,<font color="Maroon" title="c13">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:122"><span class="lab"><font color="Green" title="E74">A2</font></span></a>, <a class="ref" href="analmetr.html#T89" target="_self" title="ANALMETR:th.89">Th89</a></span>;<br/>
<a NAME="E9:122"/>
<font color="Maroon" title="c13">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:122"><span class="lab"><font color="Green" title="E73">A1</font></span></a>, <a class="txt" href="#E8:122"><span class="lab"><font color="Green" title="E76">A4</font></span></a>, <a class="ref" href="analmetr.html#D12" target="_self" title="ANALMETR:def.12">Def12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:122"/>
 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/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">p</font> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">K</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:122"><span class="lab"><font color="Green" title="E75">A3</font></span></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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