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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" 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="c7">POS</font>,<font color="Maroon" title="c10">K</font>,<font color="Maroon" title="c10">K</font>)</span><br/>

<span class="kw">assume </span><a NAME="E1:83_1_1"/>
(<font color="Maroon" title="c7">POS</font>,<font color="Maroon" title="c10">K</font>,<font color="Maroon" title="c10">K</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"> 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="E3:83_1_1"/><span class="lab"><font color="Green" title="E56">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="E4:83_1_1"/><span class="lab"><font color="Green" title="E57">A2</font></span>: 
<font color="Maroon" title="c10">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="c11">a</font>,<font color="Maroon" title="c12">b</font>)
 <span class="kw">and </span><br/><a NAME="E5:83_1_1"/><span class="lab"><font color="Green" title="E58">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>
 ;<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 <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/>
<a NAME="E7:83_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="#E4:83_1_1"><span class="lab"><font color="Green" title="E57">A2</font></span></a>, <a class="ref" href="analmetr.html#T41" target="_self" onmouseover="rs('analmetr/T41')" onmouseout="rh()">Th41</a></span>;<br/>
<a NAME="E8:83_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c11">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c10">K</font> &amp; <font color="Maroon" title="c12">b</font> <a href="tarski.html#R2" title="TARSKI: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#T15" onmouseover="rs('aff_1/T15')" onmouseout="rh()">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:83_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:83_1_1"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="#E5:83_1_1"><span class="lab"><font color="Green" title="E58">A3</font></span></a>, <a class="ref" href="analmetr.html#T51" target="_self" onmouseover="rs('analmetr/T51')" onmouseout="rh()">Th51</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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