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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>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>let </b><font color="Maroon" title="c4">seq1</font>, <font color="Maroon" title="c5">seq2</font> be   <a href="normsp_1.html#NM2" title="NORMSP_1:NM.2">sequence</a> of <font color="Maroon" title="c1">X</font>;<br/>









<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="normsp_1.html#K6" title="NORMSP_1:func.6">*</a> <span class="p2">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <font color="Maroon" title="c4">seq1</font></span>)</span></span>)</span> <a href="bhsp_1.html#K8" title="BHSP_1:func.8">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="normsp_1.html#K6" title="NORMSP_1:func.6">*</a> <span class="p2">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <font color="Maroon" title="c5">seq2</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="normsp_1.html#K6" title="NORMSP_1:func.6">*</a> <font color="Maroon" title="c4">seq1</font></span>)</span></span>)</span> <a href="bhsp_1.html#K8" title="BHSP_1:func.8">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="normsp_1.html#K6" title="NORMSP_1:func.6">*</a> <span class="p2">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <font color="Maroon" title="c5">seq2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="bhsp_4.html#T3" target="_self" title="BHSP_4:th.3">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="normsp_1.html#K6" title="NORMSP_1:func.6">*</a> <font color="Maroon" title="c4">seq1</font></span>)</span></span>)</span> <a href="bhsp_1.html#K8" title="BHSP_1:func.8">+</a> <span class="p1">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="normsp_1.html#K6" title="NORMSP_1:func.6">*</a> <font color="Maroon" title="c5">seq2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="bhsp_4.html#T3" target="_self" title="BHSP_4:th.3">Th3</a></i>
<br/>.= 
 <a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="normsp_1.html#K6" title="NORMSP_1:func.6">*</a> <font color="Maroon" title="c4">seq1</font></span>)</span> <a href="bhsp_1.html#K8" title="BHSP_1:func.8">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="normsp_1.html#K6" title="NORMSP_1:func.6">*</a> <font color="Maroon" title="c5">seq2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="bhsp_4.html#T1" target="_self" title="BHSP_4:th.1">Th1</a></i>
;<br/>


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