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<span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being   <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>  st <font color="Olive" title="b1">f</font> is  <a href="mesfunc5.html#V2" title="MESFUNC5:attr.2">nonpositive</a>  holds <br/><font color="Olive" title="b1">f</font> is  <a href="mesfunc5.html#V4" title="MESFUNC5:attr.4">without+infty</a> </span><br/><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">f</font> is  <a href="mesfunc5.html#V2" title="MESFUNC5:attr.2">nonpositive</a>  implies <font color="Maroon" title="c2">f</font> is  <a href="mesfunc5.html#V4" title="MESFUNC5:attr.4">without+infty</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:17"/>
<font color="Maroon" title="c2">f</font> is  <a href="mesfunc5.html#V2" title="MESFUNC5:attr.2">nonpositive</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> is  <a href="mesfunc5.html#V4" title="MESFUNC5:attr.4">without+infty</a> </span><br/>

<a NAME="E2:17"/><span class="kw">then </span>
 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#K12" title="SUPINF_2:func.12">.</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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfunc5.html#T8" target="_self" title="MESFUNC5:th.8">Th14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:17"/>
<font color="Maroon" title="c2">f</font> is  <a href="mesfunc5.html#V4" title="MESFUNC5:attr.4">without+infty</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mesfunc5.html#D6" target="_self" title="MESFUNC5:def.6">Def6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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