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<div><span class="kw">theorem </span><a NAME="T31"><span class="comment"><font color="firebrick">:: BHSP_3:31</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><br/>  for <font color="Olive" title="b2">seq</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">k</font>, <font color="Olive" title="b4">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">seq</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> <font color="Olive" title="b3">k</font></span>)</span> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> <font color="Olive" title="b4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">seq</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b4">m</font></span>)</span></div></div>
