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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="numbers.html#K6">ExtREAL</a> ;<br/>



<b>assume </b><a NAME="E1:22"/>
<font color="Maroon">f</font> is <a href="supinf_2.html#V6">nonnegative</a>
 ;<br/>

<a NAME="E2:22"/><b>then </b>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   holds  <a href="supinf_1.html#K2">-infty</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">f</font> <a href="mesfunc1.html#K4">.</a> <font color="Olive">x</font>
 
<b>by </b><i><a class="ref" href="supinf_2.html#T70">SUPINF_2:70</a></i>;<br/>
<b>hence </b><a NAME="E3:22"/>
<font color="Maroon">f</font> is <a href="mesfunc5.html#V3" target="_self">without-infty</a>
 <b>by </b><i/>;<br/>


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