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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" 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> 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> 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">K</font> is  <a href="analmetr.html#V5" title="ANALMETR:attr.5">being_line</a>  holds <br/> ex <font color="Olive" title="b3">x</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="b2">a</font>,<font color="Olive" title="b3">x</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Olive" title="b1">K</font> &amp; <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI: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" 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">a</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="Maroon" title="c8">K</font> is  <a href="analmetr.html#V5" title="ANALMETR:attr.5">being_line</a>  holds <br/> ex <font color="Olive" title="b2">x</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>,<font color="Olive" title="b2">x</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font> &amp; <font color="Olive" title="b2">x</font> <a href="tarski.html#R2" title="TARSKI: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> 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" 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> is  <a href="analmetr.html#V5" title="ANALMETR:attr.5">being_line</a>  implies  ex <font color="Olive" title="b1">x</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="Maroon" title="c9">a</font>,<font color="Olive" title="b1">x</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font> &amp; <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">K</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:102"/>
<font color="Maroon" title="c8">K</font> is  <a href="analmetr.html#V5" title="ANALMETR:attr.5">being_line</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">  ex <font color="Olive" title="b1">x</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="Maroon" title="c9">a</font>,<font color="Olive" title="b1">x</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font> &amp; <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI: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="c10">p</font>, <font color="Maroon" title="c11">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="E3:102"/><span class="lab"><font color="Green" title="E67">A1</font></span>: 
<font color="Maroon" title="c10">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">q</font>
 <span class="kw">and </span><br/><a NAME="E4:102"/><span class="lab"><font color="Green" title="E68">A2</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">p</font>,<font color="Maroon" title="c11">q</font>)
 ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c12">x</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="E6:102"/><span class="lab"><font color="Green" title="E69">A3</font></span>: 
<font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c12">x</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">and </span><br/><a NAME="E7:102"/><span class="lab"><font color="Green" title="E70">A4</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">p</font>,<font color="Maroon" title="c11">q</font>,<font color="Maroon" title="c12">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T69" target="_self" onmouseover="rs('analmetr/T69')" onmouseout="rh()">Th69</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c12">x</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="c9">a</font>,<font color="Maroon" title="c12">x</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font> &amp; <font color="Maroon" title="c12">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">K</font> )</span><br/>

<span class="kw">thus </span><a NAME="E8:102"/>
<font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c12">x</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c8">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:102"><span class="lab"><font color="Green" title="E67">A1</font></span></a>, <a class="txt" href="#E4:102"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E6:102"><span class="lab"><font color="Green" title="E69">A3</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"> <font color="Maroon" title="c12">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">K</font></span><br/>

<span class="kw">thus </span><a NAME="E9:102"/>
<font color="Maroon" title="c12">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:102"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E7:102"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="ref" href="analmetr.html#D11" target="_self" onmouseover="rs('analmetr/D11')" onmouseout="rh()">Def10</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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