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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th21</font></span>: <a NAME="T21"><span class="comment"><font color="firebrick">:: CLOPBAN4:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="clopban2.html#NM3" title="CLOPBAN2:NM.3">Complex_Banach_Algebra</a><br/>  for <font color="Olive" title="b2">w</font>, <font color="Olive" title="b3">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b4">k</font>, <font color="Olive" title="b5">l</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b5">l</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">k</font> holds <br/><span class="p1">(<span class="default"><a href="clopban4.html#K4" title="CLOPBAN4:func.4">Alfa</a> (<span class="p2">(<span class="default"><font color="Olive" title="b4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Olive" title="b3">z</font>,<font color="Olive" title="b2">w</font>)</span>)</span> <a href="normsp_0.html#K1" title="NORMSP_0:func.1">.</a> <font color="Olive" title="b5">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="clopban4.html#K4" title="CLOPBAN4:func.4">Alfa</a> (<font color="Olive" title="b4">k</font>,<font color="Olive" title="b3">z</font>,<font color="Olive" title="b2">w</font>)</span>)</span> <a href="normsp_0.html#K1" title="NORMSP_0:func.1">.</a> <font color="Olive" title="b5">l</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="clopban4.html#K3" title="CLOPBAN4:func.3">Expan_e</a> (<span class="p3">(<span class="default"><font color="Olive" title="b4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Olive" title="b3">z</font>,<font color="Olive" title="b2">w</font>)</span>)</span> <a href="normsp_0.html#K1" title="NORMSP_0:func.1">.</a> <font color="Olive" title="b5">l</font></span>)</span></div></div>
