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<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ,   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ) <span class="kw">-&gt; </span>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  = $1 <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> $2;<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <span class="kw">means </span>( $1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; $2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> );<br/>
<a NAME="E1:164_1_1"/>
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">r</font>,<font color="Olive" title="b2">r1</font>) where <font color="Olive" title="b1">r</font>, <font color="Olive" title="b2">r1</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font>,<font color="Olive" title="b2">r1</font>] </span>}</span>  is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="seq_4.html#S3" target="_self" title="SEQ_4:sch.3">SEQ_4:sch 3</a>();<br/></span>
<span class="kw">hence </span><a NAME="E2:164_1_1"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">r</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <font color="Olive" title="b2">r1</font></span>)</span> where <font color="Olive" title="b1">r</font>, <font color="Olive" title="b2">r1</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : ( <font color="Olive" title="b1">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b2">r1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> ) </span>}</span>  is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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