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<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">D</font>, <a href="numbers.html#K1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:67"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">d</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>  st <font color="Olive">d</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font> holds <br/><font color="Maroon">F</font> <a href="seq_1.html#K2">.</a> <font color="Olive">d</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/>

<a NAME="E2:67"/><i><font color="Green">E31</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K19" target="_self">max+</a> <font color="Maroon">F</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font>
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">d</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/><b>assume </b><a NAME="E1:67_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font>
 ;<br/><a NAME="E2:67_1"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">F</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">d</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="rfunct_3.html#E10"><i><font color="Green">Lemma45</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="rfunct_3.html#K19" target="_self">max+</a> <font color="Maroon">F</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">d</font> = 
 <a href="rfunct_3.html#K2" target="_self">max+</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">d</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">F</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">d</font>
<b>by </b><i><a class="txt" href="rfunct_3.html#E11"><i><font color="Green">Lemma48</font></i></a>, <a class="ref" href="xxreal_0.html#D9">XXREAL_0:def 9</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:67"/>
 <a href="rfunct_3.html#K19" target="_self">max+</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font>
 <b>by </b><i>, <a class="ref" href="partfun1.html#T34">PARTFUN1:34</a></i>;<br/>


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