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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E8">Th7</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: BHSP_6:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a>  st  the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Olive" title="b1">X</font> is  <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a>  &amp;  the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Olive" title="b1">X</font> is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a>  &amp;  the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Olive" title="b1">X</font> is  <a href="setwiseo.html#V1" title="SETWISEO:attr.1">having_a_unity</a>  holds <br/> for <font color="Olive" title="b2">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b2">Y</font> is  <a href="bhsp_6.html#V3" title="BHSP_6:attr.3">weakly_summable_set</a>  holds <br/> for <font color="Olive" title="b3">L</font> being   <a href="hahnban.html#NM3" title="HAHNBAN:NM.3">linear-Functional</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b3">L</font> is  <a href="bhsp_6.html#V2" title="BHSP_6:attr.2">Lipschitzian</a>  holds <br/><font color="Olive" title="b2">Y</font> <a href="bhsp_6.html#R1" title="BHSP_6:pred.1">is_summable_set_by</a> <font color="Olive" title="b3">L</font></div></div>
