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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E6">Th5</font></span>: <a NAME="T5"><span class="comment"><font color="firebrick">:: BHSP_6:5</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">S</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font>  st  not <font color="Olive" title="b2">S</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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> holds  <font color="Olive" title="b3">L</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <font color="Olive" title="b2">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> (<font color="Olive" title="b2">S</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">X</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<font color="Olive" title="b3">L</font>,<a href="binop_2.html#K9" title="BINOP_2:func.9">addreal</a>)</div></div>
