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<span class="kw">let </span><font color="Maroon" title="c10">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"> not <font color="Maroon" title="c10">K</font> <a href="analmetr.html#R7" title="ANALMETR:pred.7">_|_</a> <font color="Maroon" title="c10">K</font></span><br/>

<span class="kw">assume </span><a NAME="E1:103_1_1"/>
<font color="Maroon" title="c10">K</font> <a href="analmetr.html#R7" title="ANALMETR:pred.7">_|_</a> <font color="Maroon" title="c10">K</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">a</font>, <font color="Maroon" title="c12">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="E3:103_1_1"/><span class="lab"><font color="Green" title="E63">A1</font></span>: 
<font color="Maroon" title="c11">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font>
 <span class="kw">and </span><br/><a NAME="E4:103_1_1"/><span class="lab"><font color="Green" title="E64">A2</font></span>: 
<font color="Maroon" title="c10">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">a</font>,<font color="Maroon" title="c12">b</font>
 <span class="kw">and </span><br/><a NAME="E5:103_1_1"/><span class="lab"><font color="Green" title="E65">A3</font></span>: 
<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c10">K</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D15" target="_self" title="ANALMETR:def.15">Def15</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">a9</font> = <font color="Maroon" title="c11">a</font>, <font color="Maroon" title="c14">b9</font> = <font color="Maroon" title="c12">b</font> as   <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="c7">POS</font></span>)</span> ;<br/>
<a NAME="E7:103_1_1"/>
<font color="Maroon" title="c10">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c13">a9</font>,<font color="Maroon" title="c14">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:103_1_1"><span class="lab"><font color="Green" title="E64">A2</font></span></a>, <a class="ref" href="analmetr.html#T56" target="_self" title="ANALMETR:th.56">Th56</a></span>;<br/>
<a NAME="E8:103_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c11">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font> &amp; <font color="Maroon" title="c12">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:103_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:103_1_1"><span class="lab"><font color="Green" title="E63">A1</font></span></a>, <a class="txt" href="#E5:103_1_1"><span class="lab"><font color="Green" title="E65">A3</font></span></a>, <a class="ref" href="analmetr.html#T71" target="_self" title="ANALMETR:th.71">Th71</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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