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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/>

<b>assume </b><a NAME="E1:15"/><i><font color="Green">E13</font></i>: 
( the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="binop_1.html#V1">commutative</a> &amp; the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="binop_1.html#V2">associative</a> &amp; the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>1</sub></font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  )
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E2:15"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="bhsp_6.html#V1" target="_self">summable_set</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="hahnban.html#NM3">linear-Functional</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E3:15"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="bhsp_6.html#V2" target="_self">Bounded</a>
 ;<br/>

<a NAME="E4:15"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="bhsp_6.html#V3" target="_self">weakly_summable_set</a>
 
<b>by </b><i><a class="txt" href="bhsp_6.html#E2:15"><i><font color="Green">E14</font></i></a>, <a class="ref" href="bhsp_6.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E5:15"/>
<font color="Maroon">c<sub>2</sub></font> <a href="bhsp_6.html#R1" target="_self">is_summable_set_by</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="bhsp_6.html#E1:15"><i><font color="Green">E13</font></i></a>, <a class="txt" href="bhsp_6.html#E3:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="bhsp_6.html#T7" target="_self">Th7</a></i>;<br/>


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