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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">f</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>, <a href="numbers.html#K7" title="NUMBERS:func.7">ExtREAL</a> ;<br/>



<b>assume </b><a NAME="E1:23"/>
<font color="Maroon" title="c2">f</font> is <a href="mesfunc5.html#V2" title="MESFUNC5:attr.2">nonpositive</a>
 ;<br/>

<a NAME="E2:23"/><b>then </b>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <font color="Maroon" title="c2">f</font> <a href="supinf_2.html#K15" title="SUPINF_2:func.15">.</a> <font color="Olive" title="b1">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a> 
 
<b>by </b><i><a class="ref" href="mesfunc5.html#T14" target="_self" title="MESFUNC5:th.14">Th14</a></i>;<br/>
<b>hence </b><a NAME="E3:23"/>
<font color="Maroon" title="c2">f</font> is <a href="mesfunc5.html#V4" title="MESFUNC5:attr.4">without+infty</a>
 <b>by </b><i><a class="ref" href="mesfunc5.html#D6" target="_self" title="MESFUNC5:def.6">Def6</a></i>;<br/>


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