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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/>



<a NAME="E1:68"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K19">max+</a> <font color="Maroon">f</font></span>)</span> holds <br/>0 <a href="xxreal_0.html#R1">&lt;=</a> <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="Olive">x</font>
 
<b>by </b><i><a class="ref" href="rfunct_3.html#T40">RFUNCT_3:40</a></i>;<br/>
<b>hence </b><a NAME="E2:68"/>
 <a href="rfunct_3.html#K19">max+</a> <font color="Maroon">f</font> is <a href="supinf_2.html#V6">nonnegative</a>
 <b>by </b><i/>;<br/>

<a NAME="E3:68"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20">max-</a> <font color="Maroon">f</font></span>)</span> holds <br/>0 <a href="xxreal_0.html#R1">&lt;=</a> <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="Olive">x</font>
 
<b>by </b><i><a class="ref" href="rfunct_3.html#T43">RFUNCT_3:43</a></i>;<br/>
<b>hence </b><a NAME="E4:68"/>
 <a href="rfunct_3.html#K20">max-</a> <font color="Maroon">f</font> is <a href="supinf_2.html#V6">nonnegative</a>
 <b>by </b><i/>;<br/>


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