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<b>let </b><font color="Maroon" title="c1">seq</font> be   <a href="mesfunc5.html#NM1" title="MESFUNC5:NM.1">ExtREAL_sequence</a>;<br/><b>let </b><font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>



<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a>  = <font color="Maroon" title="c1">seq</font> <a href="mesfunc1.html#K4" title="MESFUNC1:func.4">.</a> $1;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ] <b>means </b><font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> $1;<br/>
<b>set </b><font color="Maroon" title="c3">Y</font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) where <font color="Olive" title="b1">k</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] </span>}</span> ;<br/>
<a NAME="E1:8"/><i><font color="Green" title="E9">A3</font></i>: 
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) where <font color="Olive" title="b1">k</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] </span>}</span>  is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a> 
 
<b>from </b><i><a class="ref" href="domain_1.html#S8" title="DOMAIN_1:sch.8">DOMAIN_1:sch 8</a>();<br/></i>
<a NAME="E2:8"/>
<font color="Maroon" title="c1">seq</font> <a href="mesfunc1.html#K4" title="MESFUNC1:func.4">.</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) where <font color="Olive" title="b1">k</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E3:8"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="mesfunc1.html#K4" title="MESFUNC1:func.4">.</a> <font color="Olive" title="b1">k</font></span>)</span> where <font color="Olive" title="b1">k</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  : <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> </span>}</span>  is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a> 
 <b>by </b><i><a class="txt" href="rinfsup2.html#E1:8"><i><font color="Green" title="E9">A3</font></i></a></i>;<br/>


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