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<b>set </b><font color="Maroon" title="c3">S</font> =  <a href="integra1.html#K8" title="INTEGRA1:func.8">divs</a> <font color="Maroon" title="c1">A</font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>$1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="integra1.html#K8" title="INTEGRA1:func.8">divs</a> <font color="Maroon" title="c1">A</font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="integra1.html#M3" title="INTEGRA1:mode.3">Element</a> of  <a href="integra1.html#K8" title="INTEGRA1:func.8">divs</a> <font color="Maroon" title="c1">A</font>) <b>-&gt; </b>  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> =  <a href="integra1.html#K6" title="INTEGRA1:func.6">upper_sum</a> <font color="Maroon" title="c2">f</font>,$1;<br/>
<b>consider </b><font color="Maroon" title="c4">g</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="integra1.html#K8" title="INTEGRA1:func.8">divs</a> <font color="Maroon" title="c1">A</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <b> such that </b><br/><a NAME="E2:27_1_1"/><i><font color="Green" title="E18">A1</font></i>: 
for <font color="Olive" title="b1">D</font> being   <a href="integra1.html#M3" title="INTEGRA1:mode.3">Element</a> of  <a href="integra1.html#K8" title="INTEGRA1:func.8">divs</a> <font color="Maroon" title="c1">A</font> holds <br/> ( <font color="Olive" title="b1">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">D</font>] )
 <b>and </b><br/><a NAME="E3:27_1_1"/><i><font color="Green" title="E19">A2</font></i>: 
for <font color="Olive" title="b1">D</font> being   <a href="integra1.html#M3" title="INTEGRA1:mode.3">Element</a> of  <a href="integra1.html#K8" title="INTEGRA1:func.8">divs</a> <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b1">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g</font> holds <br/><font color="Maroon" title="c4">g</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">D</font>)
 <b>from </b><i><a class="ref" href="seq_1.html#S3" title="SEQ_1:sch.3">SEQ_1:sch 3</a>();<br/></i>
<b>take </b>
<font color="Maroon" title="c4">g</font>
;<br/>

<a NAME="E4:27_1_1"/>
 <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <span class="p1">(<span class="default"><a href="integra1.html#K8" title="INTEGRA1:func.8">divs</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="integra1.html#K8" title="INTEGRA1:func.8">divs</a> <font color="Maroon" title="c1">A</font>
 
;<br/>
<b>hence </b><a NAME="E5:27_1_1"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="integra1.html#K8" title="INTEGRA1:func.8">divs</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="txt" href="integra1.html#E2:27_1_1"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="subset_1.html#T8" title="SUBSET_1:th.8">SUBSET_1:8</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">D</font> be    <a href="integra1.html#M3" title="INTEGRA1:mode.3">Element</a> of  <a href="integra1.html#K8" title="INTEGRA1:func.8">divs</a> <font color="Maroon" title="c1">A</font>;<br/><b>assume </b><a NAME="E1:27_1_1_1"/>
<font color="Maroon" title="c5">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="integra1.html#K8" title="INTEGRA1:func.8">divs</a> <font color="Maroon" title="c1">A</font>
 ;<br/><a NAME="E2:27_1_1_1"/>
<font color="Maroon" title="c5">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g</font>
 <b>by </b><i><a class="txt" href="integra1.html#E2:27_1_1"><i><font color="Green" title="E18">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E3:27_1_1_1"/>
<font color="Maroon" title="c4">g</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="integra1.html#K6" title="INTEGRA1:func.6">upper_sum</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c5">D</font>
 <b>by </b><i><a class="txt" href="integra1.html#E3:27_1_1"><i><font color="Green" title="E19">A2</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:27_1_1"/>
for <font color="Olive" title="b1">D</font> being   <a href="integra1.html#M3" title="INTEGRA1:mode.3">Element</a> of  <a href="integra1.html#K8" title="INTEGRA1:func.8">divs</a> <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b1">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g</font> holds <br/><font color="Maroon" title="c4">g</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="integra1.html#K6" title="INTEGRA1:func.6">upper_sum</a> <font color="Maroon" title="c2">f</font>,<font color="Olive" title="b1">D</font>
 ;<br/>


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