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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a>;<br/>

<b>assume </b><a NAME="E1:15"/><i><font color="Green" title="E13">A1</font></i>: 
( the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c1">X</font> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c1">X</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> &amp; the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c1">X</font> <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a>  )
 ;<br/>

<b>let </b><font color="Maroon" title="c2">Y</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/>

<b>assume </b><a NAME="E2:15"/><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c2">Y</font> is <a href="bhsp_6.html#V1" title="BHSP_6:attr.1">summable_set</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">L</font> be   <a href="hahnban.html#NM3" title="HAHNBAN:NM.3">linear-Functional</a> of <font color="Maroon" title="c1">X</font>;<br/>

<b>assume </b><a NAME="E3:15"/><i><font color="Green" title="E15">A3</font></i>: 
<font color="Maroon" title="c3">L</font> is <a href="bhsp_6.html#V2" title="BHSP_6:attr.2">Bounded</a>
 ;<br/>

<a NAME="E4:15"/>
<font color="Maroon" title="c2">Y</font> is <a href="bhsp_6.html#V3" title="BHSP_6:attr.3">weakly_summable_set</a>
 
<b>by </b><i><a class="txt" href="bhsp_6.html#E2:15"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="bhsp_6.html#T3" target="_self" title="BHSP_6:th.3">Th3</a></i>;<br/>
<b>hence </b><a NAME="E5:15"/>
<font color="Maroon" title="c2">Y</font> <a href="bhsp_6.html#R1" title="BHSP_6:pred.1">is_summable_set_by</a> <font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="txt" href="bhsp_6.html#E1:15"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="bhsp_6.html#E3:15"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="bhsp_6.html#T7" target="_self" title="BHSP_6:th.7">Th7</a></i>;<br/>


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