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<span class="kw">deffunc </span><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> ) <span class="kw">-&gt; </span>   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font> =  <a href="integr15.html#K4" title="INTEGR15:func.4">middle_sum</a> <font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="integr15.html#K5" title="INTEGR15:func.5">.</a> $1</span>)</span>;<br/>
<a NAME="E1:25_1_1"/><span class="lab"><font color="Green" title="E22">A1</font></span>: 
 <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Maroon" title="c1">n</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="real_ns1.html#D4" title="REAL_NS1:def.4">REAL_NS1:def 4</a></span>;<br/>
<a NAME="E2:25_1_1"/>
 ex <font color="Olive" title="b1">IT</font> being  <a href="nat_1.html#NM2" title="NAT_1:NM.2">sequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font></span>)</span> st <br/>for <font color="Olive" title="b2">i</font> being   <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>  holds  <font color="Olive" title="b1">IT</font> <a href="real_ns1.html#K5" title="REAL_NS1:func.5">.</a> <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">i</font>)
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S4" title="FUNCT_2:sch.4">FUNCT_2:sch 4</a>();<br/></span>
<span class="kw">hence </span><a NAME="E3:25_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Maroon" title="c1">n</font></span>)</span> st <br/>for <font color="Olive" title="b2">i</font> being   <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>  holds  <font color="Olive">b<sub>1</sub></font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="integr15.html#K4" title="INTEGR15:func.4">middle_sum</a> <font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="integr15.html#K5" title="INTEGR15:func.5">.</a> <font color="Olive" title="b2">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25_1_1"><span class="lab"><font color="Green" title="E22">A1</font></span></a></span>; <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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