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<b>let </b><font color="Maroon">X</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">X</font>, <a href="supinf_1.html#K3">REAL</a> ;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:46"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <span class="p1">(<span class="default"><a href="rfunct_3.html#K20">max-</a> <font color="Maroon">f</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font></span>)</span> )
 ;<br/>

<a NAME="E2:46"/><b>then </b>
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K2">max-</a> <span class="p2">(<span class="default"><a href="mesfunc5.html#K1">R_EAL</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">x</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:46"/><b>then </b>
 <a href="supinf_2.html#K3">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc5.html#K1">R_EAL</a> <font color="Maroon">f</font></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K2">max-</a> <span class="p2">(<span class="default"><a href="mesfunc5.html#K1">R_EAL</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="supinf_2.html#T3">SUPINF_2:3</a></i>;<br/>
<a NAME="E4:46"/><b>then </b>
<span class="p1">(<span class="default"><a href="mesfunc2.html#K1">max+</a> <span class="p2">(<span class="default"><a href="mesfunc5.html#K1">R_EAL</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K1">0.</a> 
 
<b>by </b><i>, <a class="ref" href="mesfunc2.html#T23">MESFUNC2:23</a></i>;<br/>
<b>hence </b><a NAME="E5:46"/>
<span class="p1">(<span class="default"><a href="rfunct_3.html#K19">max+</a> <font color="Maroon">f</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i/>;<br/>


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