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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#M2" title="HIDDEN:mode.2">set</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">  for <font color="Olive" title="b1">F</font> being   <a href="seqfunc.html#NM1" title="SEQFUNC:NM.1">Functional_Sequence</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  st <font color="Olive" title="b1">F</font> is  <a href="mesfunc8.html#V1" title="MESFUNC8:attr.1">with_the_same_dom</a>  holds <br/> <a href="mesfun9c.html#K3" title="MESFUN9C:func.3">Partial_Sums</a> <font color="Olive" title="b1">F</font> is  <a href="mesfunc8.html#V1" title="MESFUNC8:attr.1">with_the_same_dom</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">F</font> be   <a href="seqfunc.html#NM1" title="SEQFUNC:NM.1">Functional_Sequence</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</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="c2">F</font> is  <a href="mesfunc8.html#V1" title="MESFUNC8:attr.1">with_the_same_dom</a>  implies  <a href="mesfun9c.html#K3" title="MESFUN9C:func.3">Partial_Sums</a> <font color="Maroon" title="c2">F</font> is  <a href="mesfunc8.html#V1" title="MESFUNC8:attr.1">with_the_same_dom</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:38"/>
<font color="Maroon" title="c2">F</font> is  <a href="mesfunc8.html#V1" title="MESFUNC8:attr.1">with_the_same_dom</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="mesfun9c.html#K3" title="MESFUN9C:func.3">Partial_Sums</a> <font color="Maroon" title="c2">F</font> is  <a href="mesfunc8.html#V1" title="MESFUNC8:attr.1">with_the_same_dom</a> </span><br/>

<a NAME="E2:38"/><span class="kw">then </span>
 <a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <font color="Maroon" title="c2">F</font> is  <a href="mesfunc8.html#V1" title="MESFUNC8:attr.1">with_the_same_dom</a> 
 
;<br/>
<a NAME="E3:38"/><span class="kw">then </span>
 <a href="mesfun9c.html#K2" title="MESFUN9C:func.2">Partial_Sums</a> <span class="p1">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <font color="Maroon" title="c2">F</font></span>)</span> is  <a href="mesfunc8.html#V1" title="MESFUNC8:attr.1">with_the_same_dom</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun9c.html#T17" target="_self" onmouseover="rs('mesfun9c/T17')" onmouseout="rh()">Th17</a></span>;<br/>
<a NAME="E4:38"/><span class="kw">then </span>
 <a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <span class="p1">(<span class="default"><a href="mesfun9c.html#K3" title="MESFUN9C:func.3">Partial_Sums</a> <font color="Maroon" title="c2">F</font></span>)</span> is  <a href="mesfunc8.html#V1" title="MESFUNC8:attr.1">with_the_same_dom</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun9c.html#T29" target="_self" onmouseover="rs('mesfun9c/T29')" onmouseout="rh()">Th29</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:38"/>
 <a href="mesfun9c.html#K3" title="MESFUN9C:func.3">Partial_Sums</a> <font color="Maroon" title="c2">F</font> is  <a href="mesfunc8.html#V1" title="MESFUNC8:attr.1">with_the_same_dom</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun9c.html#T24" target="_self" onmouseover="rs('mesfun9c/T24')" onmouseout="rh()">Th24</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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