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<span class="kw">let </span><font color="Maroon" title="c7">POS</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="analmetr.html#L2" title="ANALMETR:struct.2">ParOrtStr</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">K</font>, <font color="Olive" title="b2">M</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c7">POS</font> holds <br/> ( <font color="Olive" title="b1">K</font> <a href="analmetr.html#R7" title="ANALMETR:pred.7">_|_</a> <font color="Olive" title="b2">M</font> iff  ex <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">d</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">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">b</font> &amp; <font color="Olive" title="b5">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">d</font> &amp; <font color="Olive" title="b1">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>) &amp; <font color="Olive" title="b2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Olive" title="b5">c</font>,<font color="Olive" title="b6">d</font>) &amp; <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b5">c</font>,<font color="Olive" title="b6">d</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c8">K</font>, <font color="Maroon" title="c9">M</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">K</font> <a href="analmetr.html#R7" title="ANALMETR:pred.7">_|_</a> <font color="Maroon" title="c9">M</font> iff  ex <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="c7">POS</font> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">d</font> &amp; <font color="Maroon" title="c8">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) &amp; <font color="Maroon" title="c9">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</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="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> ) )</span><br/>





<div><span class="kw">hereby </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"> (  ex <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="c7">POS</font> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">d</font> &amp; <font color="Maroon" title="c8">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) &amp; <font color="Maroon" title="c9">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</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="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> ) implies <font color="Maroon" title="c8">K</font> <a href="analmetr.html#R7" title="ANALMETR:pred.7">_|_</a> <font color="Maroon" title="c9">M</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:75_1"/>
<font color="Maroon" title="c8">K</font> <a href="analmetr.html#R7" title="ANALMETR:pred.7">_|_</a> <font color="Maroon" title="c9">M</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">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="c7">POS</font> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">d</font> &amp; <font color="Maroon" title="c8">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) &amp; <font color="Maroon" title="c9">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</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="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> )</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c11">b</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="E3:75_1"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
( <font color="Maroon" title="c10">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">b</font> &amp; <font color="Maroon" title="c8">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font>) )
 <span class="kw">and </span><br/><a NAME="E4:75_1"/><span class="lab"><font color="Green" title="E54">A2</font></span>: 
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c9">M</font>
 ;<br/><a NAME="E5:75_1"/>
 ex <font color="Olive" title="b1">c</font>, <font color="Olive" title="b2">d</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">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">d</font> &amp; <font color="Maroon" title="c9">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Olive" title="b1">c</font>,<font color="Olive" title="b2">d</font>) &amp; <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b1">c</font>,<font color="Olive" title="b2">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:75_1"><span class="lab"><font color="Green" title="E54">A2</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E6:75_1"/>
 ex <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="c7">POS</font> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">d</font> &amp; <font color="Maroon" title="c8">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) &amp; <font color="Maroon" title="c9">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</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="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:75_1"><span class="lab"><font color="Green" title="E53">A1</font></span></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/></div>
<span class="kw">end;</span></div>

<span class="kw">given </span><font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c11">b</font>, <font color="Maroon" title="c12">c</font>, <font color="Maroon" title="c13">d</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><a NAME="E3:75"/><span class="lab"><font color="Green" title="E53">A3</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">b</font>
 <span class="kw">and </span><br/><a NAME="E4:75"/><span class="lab"><font color="Green" title="E54">A4</font></span>: 
<font color="Maroon" title="c12">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font>
 <span class="kw">and </span><br/><a NAME="E5:75"/><span class="lab"><font color="Green" title="E55">A5</font></span>: 
<font color="Maroon" title="c8">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font>)
 <span class="kw">and </span><br/><a NAME="E6:75"/><span class="lab"><font color="Green" title="E56">A6</font></span>: 
( <font color="Maroon" title="c9">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Maroon" title="c12">c</font>,<font color="Maroon" title="c13">d</font>) &amp; <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">c</font>,<font color="Maroon" title="c13">d</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">K</font> <a href="analmetr.html#R7" title="ANALMETR:pred.7">_|_</a> <font color="Maroon" title="c9">M</font></span><br/>

<a NAME="E7:75"/>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c9">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:75"><span class="lab"><font color="Green" title="E54">A4</font></span></a>, <a class="txt" href="#E6:75"><span class="lab"><font color="Green" title="E56">A6</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:75"/>
<font color="Maroon" title="c8">K</font> <a href="analmetr.html#R7" title="ANALMETR:pred.7">_|_</a> <font color="Maroon" title="c9">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:75"><span class="lab"><font color="Green" title="E53">A3</font></span></a>, <a class="txt" href="#E5:75"><span class="lab"><font color="Green" title="E55">A5</font></span></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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