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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">M</font>, <font color="Olive" title="b2">N</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="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 <font color="Olive" title="b3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b4">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <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="b1">M</font> is  <a href="analmetr.html#V5" title="ANALMETR:attr.5">being_line</a>  &amp; <font color="Olive" title="b5">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Olive" title="b6">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">N</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="b2">N</font> is  <a href="analmetr.html#V5" title="ANALMETR:attr.5">being_line</a>  &amp; <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">c</font>,<font color="Olive" title="b6">d</font> holds <br/><font color="Olive" title="b1">M</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Olive" title="b2">N</font></span><br/><span class="kw">let </span><font color="Maroon" title="c8">M</font>, <font color="Maroon" title="c9">N</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>, <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 <font color="Olive" title="b1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <font color="Olive" title="b2">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <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="Maroon" title="c8">M</font> is  <a href="analmetr.html#V5" title="ANALMETR:attr.5">being_line</a>  &amp; <font color="Olive" title="b3">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">N</font> &amp; <font color="Olive" title="b4">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">N</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="c9">N</font> is  <a href="analmetr.html#V5" title="ANALMETR:attr.5">being_line</a>  &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> holds <br/><font color="Maroon" title="c8">M</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">N</font></span><br/><span class="kw">let </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> 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="c10">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <font color="Maroon" title="c11">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <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">M</font> is  <a href="analmetr.html#V5" title="ANALMETR:attr.5">being_line</a>  &amp; <font color="Maroon" title="c12">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">N</font> &amp; <font color="Maroon" title="c13">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">N</font> &amp; <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> &amp; <font color="Maroon" title="c9">N</font> is  <a href="analmetr.html#V5" title="ANALMETR:attr.5">being_line</a>  &amp; <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">c</font>,<font color="Maroon" title="c13">d</font> implies <font color="Maroon" title="c8">M</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">N</font> )</span><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:96"/><span class="lab"><font color="Green" title="E64">A1</font></span>: 
( <font color="Maroon" title="c10">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <font color="Maroon" title="c11">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">M</font> )
 <span class="kw">and </span><br/><a NAME="E2:96"/><span class="lab"><font color="Green" title="E65">A2</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="E3:96"/><span class="lab"><font color="Green" title="E66">A3</font></span>: 
( <font color="Maroon" title="c8">M</font> is  <a href="analmetr.html#V5" title="ANALMETR:attr.5">being_line</a>  &amp; <font color="Maroon" title="c12">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">N</font> &amp; <font color="Maroon" title="c13">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">N</font> )
 <span class="kw">and </span><br/><a NAME="E4:96"/><span class="lab"><font color="Green" title="E67">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="E5:96"/><span class="lab"><font color="Green" title="E68">A5</font></span>: 
<font color="Maroon" title="c9">N</font> is  <a href="analmetr.html#V5" title="ANALMETR:attr.5">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E6:96"/><span class="lab"><font color="Green" title="E69">A6</font></span>: 
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</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">M</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">N</font></span><br/>

<a NAME="E7:96"/>
( <font color="Maroon" title="c8">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="c10">a</font>,<font color="Maroon" title="c11">b</font>) &amp; <font color="Maroon" title="c9">N</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>) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:96"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="txt" href="#E2:96"><span class="lab"><font color="Green" title="E65">A2</font></span></a>, <a class="txt" href="#E3:96"><span class="lab"><font color="Green" title="E66">A3</font></span></a>, <a class="txt" href="#E4:96"><span class="lab"><font color="Green" title="E67">A4</font></span></a>, <a class="txt" href="#E5:96"><span class="lab"><font color="Green" title="E68">A5</font></span></a>, <a class="ref" href="analmetr.html#T54" target="_self" onmouseover="rs('analmetr/T54')" onmouseout="rh()">Th54</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:96"/>
<font color="Maroon" title="c8">M</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:96"><span class="lab"><font color="Green" title="E65">A2</font></span></a>, <a class="txt" href="#E4:96"><span class="lab"><font color="Green" title="E67">A4</font></span></a>, <a class="txt" href="#E6:96"><span class="lab"><font color="Green" title="E69">A6</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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