<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T42"><span class="comment"><font color="firebrick">:: LOPBAN_3:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="lopban_2.html#NM3" title="LOPBAN_2:NM.3">Banach_Algebra</a><br/>  for <font color="Olive" title="b2">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">X</font>  st <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"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b1">X</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b2">x</font></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> 1 holds <br/>( <font color="Olive" title="b2">x</font> is  <a href="algstr_0.html#V25" title="ALGSTR_0:attr.25">invertible</a>  &amp; <font color="Olive" title="b2">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lopban_3.html#K1" title="LOPBAN_3:func.1">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b1">X</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b2">x</font></span>)</span> <a href="lopban_3.html#K5" title="LOPBAN_3:func.5">GeoSeq</a></span>)</span> )</div></div>
