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<b>let </b><font color="Maroon">c<sub>1</sub></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/>

<b>assume </b><a NAME="E1:94"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="supinf_2.html#V6" target="_self">nonnegative</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<a NAME="E2:94"/>
<font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="supinf_2.html#D16" target="_self">Def16</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> ;<br/>
<a NAME="E4:94"/><i><font color="Green">E69</font></i>: 
 <a href="supinf_2.html#K18" target="_self">Ser</a> <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="supinf_2.html#D21" target="_self">Def21</a></i>;<br/>
<a NAME="E5:94"/>
 <a href="supinf_2.html#K17" target="_self">rng</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="supinf_2.html#NM2">Pos_Denum_Set_of_R_EAL</a>
 
<b>by </b><i><a class="txt" href="supinf_2.html#E1:94"><i><font color="Green">E68</font></i></a>, <a class="ref" href="supinf_2.html#D22" target="_self">Def22</a></i>;<br/>
<b>hence </b><a NAME="E6:94"/>
<span class="p1">(<span class="default"><a href="supinf_2.html#K18" target="_self">Ser</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="supinf_2.html#K13" target="_self">.</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K18" target="_self">Ser</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="supinf_2.html#K13" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="supinf_2.html#E4:94"><i><font color="Green">E69</font></i></a>, <a class="ref" href="supinf_2.html#T56" target="_self">Th56</a></i>;<br/>


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