<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">POS</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="analmetr.html#L1" target="_self">ParOrtStr</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font>;<br/><b>let </b><font color="Maroon">K</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">POS</font>;<br/><b>let </b><font color="Maroon">M</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">POS</font>;<br/>









<div><i><font color="Green">E38</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font>;<br/><b>let </b><font color="Maroon">K</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">POS</font>;<br/><b>assume </b><a NAME="E1:75_1"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analmetr.html#R6" target="_self">_|_</a> <font color="Maroon">K</font>
 ;<br/><a NAME="E2:75_1"/><b>then </b>
 ex <font color="Olive">p</font>, <font color="Olive">q</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font> st <br/>( <font color="Olive">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">q</font> &amp; <font color="Maroon">K</font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K4" target="_self">Line</a> <font color="Olive">p</font>,<font color="Olive">q</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">p</font>,<font color="Olive">q</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T9" target="_self">Th9</a></i>;<br/><b>hence </b><a NAME="E3:75_1"/>
<font color="Maroon">K</font> is <a href="analmetr.html#V4" target="_self">being_line</a>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:75_2"/>
<font color="Maroon">K</font> <a href="analmetr.html#R7" target="_self">_|_</a> <font color="Maroon">M</font>
 ;<br/><a NAME="E2:75_2"/><b>then </b><i><font color="Green">E39</font></i>: 
 ex <font color="Olive">p</font>, <font color="Olive">q</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font> st <br/>( <font color="Olive">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">q</font> &amp; <font color="Maroon">K</font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K4" target="_self">Line</a> <font color="Olive">p</font>,<font color="Olive">q</font> &amp; <font color="Olive">p</font>,<font color="Olive">q</font> <a href="analmetr.html#R6" target="_self">_|_</a> <font color="Maroon">M</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T10" target="_self">Th10</a></i>;<br/><b>hence </b><a NAME="E3:75_2"/>
<font color="Maroon">K</font> is <a href="analmetr.html#V4" target="_self">being_line</a>
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E4:75_2"/>
<font color="Maroon">M</font> is <a href="analmetr.html#V4" target="_self">being_line</a>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T13" target="_self">Th13</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:75"/>
( ( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analmetr.html#R6" target="_self">_|_</a> <font color="Maroon">K</font> implies <font color="Maroon">K</font> is <a href="analmetr.html#V4" target="_self">being_line</a> ) &amp; ( <font color="Maroon">K</font> <a href="analmetr.html#R7" target="_self">_|_</a> <font color="Maroon">M</font> implies ( <font color="Maroon">K</font> is <a href="analmetr.html#V4" target="_self">being_line</a> &amp; <font color="Maroon">M</font> is <a href="analmetr.html#V4" target="_self">being_line</a> ) ) )
 <b>by </b><i/>;<br/>


</div>
