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

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  =  <a href="card_1.html#K4">card</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">s</font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">t</font>) where <font color="Olive">t</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">t</font>] </span>}</span> ;<br/>
<b>consider </b><font color="Maroon">t</font> being    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font>;<br/>
<a NAME="E2:19_1_1"/><i><font color="Green">E30</font></i>: 
 <a href="card_1.html#K4">card</a> <font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">t</font>) where <font color="Olive">t</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">t</font>] </span>}</span> 
 
;<br/>
<a NAME="E3:19_1_1"/><i><font color="Green">E32</font></i>: 
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">t</font>) where <font color="Olive">t</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">t</font>] </span>}</span>  is   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K5">NAT</a> 
 
<b>from </b><i><a class="ref" href="domain_1.html#S8">DOMAIN_1:sch 8</a>();<br/></i>
<a NAME="E4:19_1_1"/>
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">t</font>) where <font color="Olive">t</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">t</font>] </span>}</span>  is <a href="finset_1.html#V1">finite</a>
 
<b>from </b><i><a class="ref" href="pre_circ.html#S1">PRE_CIRC:sch 1</a>();<br/></i>
<b>then reconsider </b><font color="Maroon">s</font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">t</font>) where <font color="Olive">t</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">t</font>] </span>}</span>  as  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, </i>;<br/>
<b>take </b>
 <a href="pre_circ.html#K1">max</a> <font color="Maroon">s</font>
;<br/>

<b>take </b>
<font color="Maroon">s</font>
;<br/>

<b>thus </b><a NAME="E6:19_1_1"/>
( <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Olive">t</font></span>)</span> where <font color="Olive">t</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font> : verum </span>}</span>  &amp;  <a href="pre_circ.html#K1">max</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="pre_circ.html#K1">max</a> <font color="Maroon">s</font> )
 ;<br/>


</div>
