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<span class="kw">let </span><font color="Maroon" title="c1">F</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">F</font> is  <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">nonnegative</a>  implies  <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="supinf_2.html#K14" title="SUPINF_2:func.14">SUM</a> <font color="Maroon" title="c1">F</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:2"/>
<font color="Maroon" title="c1">F</font> is  <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">nonnegative</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="supinf_2.html#K14" title="SUPINF_2:func.14">SUM</a> <font color="Maroon" title="c1">F</font></span><br/>

<a NAME="E2:2"/><span class="kw">then </span>
 <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K13" title="SUPINF_2:func.13">Ser</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="supinf_2.html#T40" onmouseover="rs('supinf_2/T40')" onmouseout="rh()">SUPINF_2:40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:2"/>
 <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="supinf_2.html#K14" title="SUPINF_2:func.14">SUM</a> <font color="Maroon" title="c1">F</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T4" onmouseover="rs('funct_2/T4')" onmouseout="rh()">FUNCT_2:4</a>, <a class="ref" href="xxreal_2.html#T4" onmouseover="rs('xxreal_2/T4')" onmouseout="rh()">XXREAL_2:4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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