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<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <a href="numbers.html#K7" title="NUMBERS:func.7">ExtREAL</a> ;<br/>

<b>assume </b><a NAME="E1:96"/><i><font color="Green" title="E68">A1</font></i>: 
<font color="Maroon" title="c1">F</font> is <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">nonnegative</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">n</font>, <font color="Maroon" title="c3">m</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>reconsider </b><font color="Maroon" title="c4">N</font> = <font color="Maroon" title="c1">F</font> as    <a href="supinf_2.html#M1" title="SUPINF_2:mode.1">Num</a> of  <a href="supinf_2.html#K19" title="SUPINF_2:func.19">rng</a> <font color="Maroon" title="c1">F</font> <b>by </b><i><a class="ref" href="supinf_2.html#D16" target="_self" title="SUPINF_2:def.16">Def16</a></i>;<br/>
<a NAME="E3:96"/><i><font color="Green" title="E69">A2</font></i>: 
 <a href="supinf_2.html#K20" title="SUPINF_2:func.20">Ser</a> <font color="Maroon" title="c1">F</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="supinf_2.html#K16" title="SUPINF_2:func.16">Ser</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K19" title="SUPINF_2:func.19">rng</a> <font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c4">N</font>
 
<b>by </b><i><a class="ref" href="supinf_2.html#D21" target="_self" title="SUPINF_2:def.21">Def21</a></i>;<br/>
<a NAME="E4:96"/>
 <a href="supinf_2.html#K19" title="SUPINF_2:func.19">rng</a> <font color="Maroon" title="c1">F</font> is   <a href="supinf_2.html#NM2" title="SUPINF_2:NM.2">Pos_Denum_Set_of_R_EAL</a>
 
<b>by </b><i><a class="txt" href="supinf_2.html#E1:96"><i><font color="Green" title="E68">A1</font></i></a>, <a class="ref" href="supinf_2.html#D22" target="_self" title="SUPINF_2:def.22">Def22</a></i>;<br/>
<b>hence </b><a NAME="E5:96"/>
<span class="p1">(<span class="default"><a href="supinf_2.html#K20" title="SUPINF_2:func.20">Ser</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="supinf_2.html#K15" title="SUPINF_2:func.15">.</a> <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K20" title="SUPINF_2:func.20">Ser</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="supinf_2.html#K15" title="SUPINF_2:func.15">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">m</font></span>)</span>
 <b>by </b><i><a class="txt" href="supinf_2.html#E3:96"><i><font color="Green" title="E69">A2</font></i></a>, <a class="ref" href="supinf_2.html#T56" target="_self" title="SUPINF_2:th.56">Th56</a></i>;<br/>


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