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<div><span class="kw">theorem </span><a NAME="T29"><span class="comment"><font color="firebrick">:: RUSUB_7:29</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">K</font> being   <a href="bhsp_1.html#V1" title="BHSP_1:attr.1">strict</a>   <a href="rusub_1.html#M1" title="RUSUB_1:mode.1">Subspace</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">M</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <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="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">K</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> &amp;  <a href="rusub_3.html#K1" title="RUSUB_3:func.1">Lin</a> <font color="Olive" title="b3">M</font> is    <a href="rusub_1.html#M1" title="RUSUB_1:mode.1">Subspace</a> of <font color="Olive" title="b2">K</font> holds <br/> <a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <span class="p1">(<span class="default"><a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Olive" title="b3">M</font></span>)</span> is    <a href="rusub_1.html#M1" title="RUSUB_1:mode.1">Subspace</a> of <font color="Olive" title="b2">K</font></div></div>
