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

<a NAME="E1:30_1_1"/>
<font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">O</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">q</font>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E2:30_1_1"/><b>then </b>
<font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">O</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K5">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font>,<font color="Olive">a</font>,<font color="Olive">b</font></span><a href="domain_1.html#K5">]</a></span> where <font color="Olive">x</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>, <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>, <font color="Olive">a</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Olive">b</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Maroon">d</font> <a href="lattice5.html#K4">.</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">a</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">b</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="lattice5.html#D14">LATTICE5:def 14</a></i>;<br/>
<b>then consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>, <font color="Maroon">y</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>, <font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E4:30_1_1"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">O</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K5">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="domain_1.html#K5">]</a></span> &amp; <font color="Maroon">d</font> <a href="lattice5.html#K4">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">a</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">b</font> )
 ;<br/>
<a NAME="E5:30_1_1"/><i><font color="Green">E58</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 
;<br/>
<a NAME="E6:30_1_1"/>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">A</font>,<font color="Maroon">O</font>
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font>, <font color="Maroon">y</font> = <font color="Maroon">y</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">A</font>,<font color="Maroon">O</font> <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">a</font>, <font color="Maroon">b</font> = <font color="Maroon">b</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> ;<br/>
<b>reconsider </b><font color="Maroon">z</font> = <span class="p1"><a href="domain_1.html#K5">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="domain_1.html#K5">]</a></span> as    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">A</font>,<font color="Maroon">O</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">A</font>,<font color="Maroon">O</font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font></span><a href="zfmisc_1.html#K4">:]</a></span> ;<br/>
<a NAME="E10:30_1_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">O</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E11:30_1_1"/>
<font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">O</font> is    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">A</font>,<font color="Maroon">O</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">A</font>,<font color="Maroon">O</font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font></span><a href="zfmisc_1.html#K4">:]</a></span>
 ;<br/>


</div>
