<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E24">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: RUSUB_7:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="rsspace2.html#NM1" title="RSSPACE2:NM.1">RealHilbertSpace</a><br/>  for <font color="Olive" title="b2">M</font> being    <a href="rusub_1.html#M1" title="RUSUB_1:mode.1">Subspace</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b1">X</font> is  <a href="bhsp_1.html#V1" title="BHSP_1:attr.1">strict</a>  &amp;  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">M</font> is   <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="normsp_2.html#K3" title="NORMSP_2:func.3">TopSpaceNorm</a> <span class="p2">(<span class="default"><a href="dualsp04.html#K2" title="DUALSP04:func.2">RUSp2RNSp</a> <font color="Olive" title="b1">X</font></span>)</span></span>)</span> holds <br/><font color="Olive" title="b1">X</font> <a href="rusub_2.html#R1" title="RUSUB_2:pred.1">is_the_direct_sum_of</a> <font color="Olive" title="b2">M</font>, <a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <font color="Olive" title="b2">M</font></div></div>
