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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>let </b><font color="Maroon">d</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/>





<a NAME="E1:56"/><i><font color="Green">E30</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <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>
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:56_1"/>
( <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> or  not <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> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_1"><b>suppose </b></a><a NAME="E1:56_1_1"/>
<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/><div class="add"><b>then </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><a class="ref" href="rfunct_3.html#T5" target="_self">Th5</a>, </i>
<br/>.= 
 <a href="xxreal_0.html#K4">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>,0

;<br/><b>hence </b><a NAME="E3:56_1_1"/>
0 <a href="xxreal_0.html#R1">&lt;=</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="seq_1.html#K2">.</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="square_1.html#T46">SQUARE_1:46</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_2"><b>suppose </b></a><a NAME="E1:56_1_2"/>
not <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/><div class="add"><b>hence </b><a NAME="E2:56_1_2"/>
0 <a href="xxreal_0.html#R1">&lt;=</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="seq_1.html#K2">.</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="rfunct_3.html#T5" target="_self">Th5</a>, <a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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