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<b>let </b><font color="Maroon">f</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:71_1"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">y</font> being  <a href="real_1.html#NM1">Real</a>  st <font color="Olive">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> holds <br/><font color="Olive">y</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:71_1_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font>
 ;<br/><a NAME="E2:71_1_1"/><b>then </b>
<font color="Maroon">f</font> <a href="goboard1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>hence </b><a NAME="E3:71_1_1"/>
<font color="Maroon">f</font> <a href="goboard1.html#K1">.</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i/>;<br/></div>
<b>end;</b></div></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:71"/><i><font color="Green">E45</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font> holds <br/><font color="Maroon">f</font> <a href="goboard1.html#K1">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>assume </b><a NAME="E1:71_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font>
 ;<br/><b>then consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:71_2"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>thus </b><a NAME="E4:71_2"/>
<font color="Maroon">x</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i>, <a class="ref" href="graph_5.html#T6" target="_self">Th6</a></i>;<br/></div>
<b>end;</b></div>


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