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

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  =  <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">IFEQ</a> $1,<font color="Maroon" title="c2">X</font>,$1,<span class="p1">(<span class="default">$1 <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c3">X0</font></span>)</span>;<br/>
<a NAME="E1:58_1_1"/><i><font color="Green" title="E43">A1</font></i>: 
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">X</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font>
 
<b>by </b><i><a class="ref" href="funcop_1.html#D8" title="FUNCOP_1:def.8">FUNCOP_1:def 8</a></i>;<br/>
<a NAME="E2:58_1_1"/><i><font color="Green" title="E44">A2</font></i>: 
for <font color="Olive" title="b1">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X</font> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">A</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">A</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X</font>;<br/>

<a NAME="E1:58_1_1_1"/>
( <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> or <font color="Maroon" title="c4">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">X</font> )
 
;<br/>
<a NAME="E2:58_1_1_1"/><b>then </b>
( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A</font> or <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font> )
 
<b>by </b><i><a class="ref" href="funcop_1.html#D8" title="FUNCOP_1:def.8">FUNCOP_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E3:58_1_1_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:58_1_1"/><i><font color="Green" title="E45">A3</font></i>: 
for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X</font> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">A</font>) <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">B</font>)
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">A</font>, <font color="Maroon" title="c5">B</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X</font>;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:58_1_1_2_1"/>
( <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> or <font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> or ( <font color="Maroon" title="c4">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c5">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">X</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_2_1_1"><b>suppose </b></a><a NAME="E1:58_1_1_2_1_1"/><i><font color="Green" title="E46">A4</font></i>: 
( <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> or <font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> )
 ;<br/><div class="add"><a NAME="E2:58_1_1_2_1_1"/>
( ( <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> or <font color="Maroon" title="c4">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">X</font> ) &amp; ( <font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> or <font color="Maroon" title="c5">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">X</font> ) )
 ;<br/><a NAME="E3:58_1_1_2_1_1"/><b>then </b>
( ( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A</font> or <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font> ) &amp; <font color="Maroon" title="c4">A</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A</font> &amp; <font color="Maroon" title="c5">B</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">B</font> &amp; ( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">B</font> or <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">B</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font> ) )
 <b>by </b><i><a class="ref" href="funcop_1.html#D8" title="FUNCOP_1:def.8">FUNCOP_1:def 8</a>, <a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/><a NAME="E4:58_1_1_2_1_1"/><b>then </b>
( <font color="Maroon" title="c4">A</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A</font> &amp; <font color="Maroon" title="c5">B</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">B</font> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>) <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>) &amp; <font color="Maroon" title="c2">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">B</font>) )
 <b>by </b><i><a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></i>;<br/><b>hence </b><a NAME="E5:58_1_1_2_1_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>) <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">B</font>)
 <b>by </b><i><a class="txt" href="topgen_3.html#E1:58_1_1_2_1_1"><i><font color="Green" title="E46">A4</font></i></a>, <a class="ref" href="funcop_1.html#D8" title="FUNCOP_1:def.8">FUNCOP_1:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_2_1_2"><b>suppose </b></a><a NAME="E1:58_1_1_2_1_2"/><i><font color="Green" title="E46">A5</font></i>: 
( <font color="Maroon" title="c4">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c5">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">X</font> )
 ;<br/><div class="add"><a NAME="E2:58_1_1_2_1_2"/>
<font color="Maroon" title="c4">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T22" title="XBOOLE_1:th.22">XBOOLE_1:22</a></i>;<br/><a NAME="E3:58_1_1_2_1_2"/><b>then </b>
<font color="Maroon" title="c4">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">X</font>
 <b>by </b><i><a class="txt" href="topgen_3.html#E1:58_1_1_2_1_2"><i><font color="Green" title="E46">A5</font></i></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>;<br/><a NAME="E4:58_1_1_2_1_2"/><b>then </b><i><font color="Green" title="E47">A6</font></i>: 
( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">B</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font> &amp; <font color="Maroon" title="c3">X0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">X0</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c3">X0</font> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">B</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font> )
 <b>by </b><i><a class="txt" href="topgen_3.html#E1:58_1_1_2_1_2"><i><font color="Green" title="E46">A5</font></i></a>, <a class="ref" href="funcop_1.html#D8" title="FUNCOP_1:def.8">FUNCOP_1:def 8</a></i>;<br/><a NAME="E5:58_1_1_2_1_2"/><b>then </b>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">B</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>;<br/><a NAME="E6:58_1_1_2_1_2"/><b>then </b>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">B</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>;<br/><b>hence </b><a NAME="E7:58_1_1_2_1_2"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>) <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">B</font>)
 <b>by </b><i><a class="txt" href="topgen_3.html#E4:58_1_1_2_1_2"><i><font color="Green" title="E47">A6</font></i></a>, <a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E4:58_1_1"/><i><font color="Green" title="E46">A7</font></i>: 
for <font color="Olive" title="b1">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X</font> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">A</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">A</font>)
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">A</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X</font>;<br/>

<a NAME="E1:58_1_1_3"/>
( <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> or <font color="Maroon" title="c4">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">X</font> )
 
;<br/>
<a NAME="E2:58_1_1_3"/><b>then </b>
( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> or ( <font color="Maroon" title="c4">A</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font> ) )
 
<b>by </b><i><a class="ref" href="funcop_1.html#D8" title="FUNCOP_1:def.8">FUNCOP_1:def 8</a></i>;<br/>
<a NAME="E3:58_1_1_3"/><b>then </b>
( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>) or ( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font> &amp; <font color="Maroon" title="c3">X0</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c3">X0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">X0</font> ) )
 
<b>by </b><i><a class="ref" href="funcop_1.html#D8" title="FUNCOP_1:def.8">FUNCOP_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E4:58_1_1_3"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">A</font>)
 <b>by </b><i><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c4">T</font> being  <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a><b> such that </b><br/><a NAME="E6:58_1_1"/><i><font color="Green" title="E47">A8</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> &amp; ( for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c4">T</font> holds   <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">A</font>) ) )
 <b>from </b><i><a class="ref" href="topgen_3.html#S3" target="_self" title="TOPGEN_3:sch.3">TOPGEN_3:sch 3</a>(<a class="txt" href="topgen_3.html#E1:58_1_1"><i><font color="Green" title="E43">A1</font></i></a>, <a class="txt" href="topgen_3.html#E2:58_1_1"><i><font color="Green" title="E44">A2</font></i></a>, <a class="txt" href="topgen_3.html#E3:58_1_1"><i><font color="Green" title="E45">A3</font></i></a>, <a class="txt" href="topgen_3.html#E4:58_1_1"><i><font color="Green" title="E46">A7</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon" title="c4">T</font>
;<br/>

<b>thus </b><a NAME="E7:58_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font>
 <b>by </b><i><a class="txt" href="topgen_3.html#E6:58_1_1"><i><font color="Green" title="E47">A8</font></i></a></i>;<br/>

<b>let </b><font color="Maroon" title="c5">F</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c4">T</font>;<br/>

<b>thus </b><a NAME="E8:58_1_1"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funcop_1.html#K15" title="FUNCOP_1:func.15">IFEQ</a> <font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c5">F</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c3">X0</font></span>)</span>
 <b>by </b><i><a class="txt" href="topgen_3.html#E6:58_1_1"><i><font color="Green" title="E47">A8</font></i></a></i>;<br/>


</div>
