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<b>let </b><font color="Maroon">F</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> , <a href="numbers.html#K6">ExtREAL</a> ;<br/>

<a NAME="E1:97"/>
<font color="Maroon">F</font> is    <a href="supinf_2.html#M1" target="_self">Num</a> of  <a href="supinf_2.html#K17" target="_self">rng</a> <font color="Maroon">F</font>
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">N</font> = <font color="Maroon">F</font> as    <a href="supinf_2.html#M1" target="_self">Num</a> of  <a href="supinf_2.html#K17" target="_self">rng</a> <font color="Maroon">F</font> ;<br/>
<a NAME="E3:97"/>
 <a href="supinf_2.html#K18" target="_self">Ser</a> <font color="Maroon">F</font> <a href="funct_2.html#R2">=</a>  <a href="supinf_2.html#K14" target="_self">Ser</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K17" target="_self">rng</a> <font color="Maroon">F</font></span>)</span>,<font color="Maroon">N</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:97"/>
( <span class="p1">(<span class="default"><a href="supinf_2.html#K18" target="_self">Ser</a> <font color="Maroon">F</font></span>)</span> <a href="supinf_2.html#K13" target="_self">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="supinf_2.html#K13" target="_self">.</a> 0 &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <br/> for <font color="Olive">y</font> being  <a href="supinf_1.html#NM3">R_eal</a>  st <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K18" target="_self">Ser</a> <font color="Maroon">F</font></span>)</span> <a href="supinf_2.html#K13" target="_self">.</a> <font color="Olive">n</font> holds <br/><span class="p1">(<span class="default"><a href="supinf_2.html#K18" target="_self">Ser</a> <font color="Maroon">F</font></span>)</span> <a href="supinf_2.html#K13" target="_self">.</a> <span class="p1">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">y</font> <a href="supinf_2.html#K2" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="supinf_2.html#K13" target="_self">.</a> <span class="p2">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) )
 <b>by </b><i/>;<br/>


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