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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E69">Th65</font></span>: <a NAME="T65"><span class="comment"><font color="firebrick">:: LPSPACE2:65</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b2">Sq</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b2">Sq</font> is  <a href="rsspace3.html#NV2" title="RSSPACE3:NV.2">Cauchy_sequence_by_Norm</a>  holds <br/> ex <font color="Olive" title="b3">N</font> being  <a href="valued_0.html#V5" title="VALUED_0:attr.5">V174</a>() <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> st <br/> for <font color="Olive" title="b4">i</font>, <font color="Olive" title="b5">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b5">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b3">N</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b4">i</font> holds <br/><span class="p1"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">Sq</font> <a href="normsp_0.html#K1" title="NORMSP_0:func.1">.</a> <font color="Olive" title="b5">j</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">Sq</font> <a href="normsp_0.html#K1" title="NORMSP_0:func.1">.</a> <span class="p4">(<span class="default"><font color="Olive" title="b3">N</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b4">i</font></span>)</span></span>)</span></span>)</span></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2 <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Olive" title="b4">i</font></span>)</span></div></div>
