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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E41">Th34</font></span>: <a NAME="T34"><span class="comment"><font color="firebrick">:: CLOPBAN4:34</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">z1</font>, <font color="Olive" title="b3">z2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b2">z1</font>,<font color="Olive" title="b3">z2</font> <a href="lopban_4.html#R1" title="LOPBAN_4:pred.1">are_commutative</a>  holds <br/>(  <a href="clopban4.html#K7" title="CLOPBAN4:func.7">exp</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">z1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b3">z2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="clopban4.html#K7" title="CLOPBAN4:func.7">exp</a> <font color="Olive" title="b2">z1</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="clopban4.html#K7" title="CLOPBAN4:func.7">exp</a> <font color="Olive" title="b3">z2</font></span>)</span> &amp;  <a href="clopban4.html#K7" title="CLOPBAN4:func.7">exp</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">z2</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">z1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="clopban4.html#K7" title="CLOPBAN4:func.7">exp</a> <font color="Olive" title="b3">z2</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="clopban4.html#K7" title="CLOPBAN4:func.7">exp</a> <font color="Olive" title="b2">z1</font></span>)</span> &amp;  <a href="clopban4.html#K7" title="CLOPBAN4:func.7">exp</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">z1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b3">z2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="clopban4.html#K7" title="CLOPBAN4:func.7">exp</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">z2</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">z1</font></span>)</span> &amp;  <a href="clopban4.html#K7" title="CLOPBAN4:func.7">exp</a> <font color="Olive" title="b2">z1</font>, <a href="clopban4.html#K7" title="CLOPBAN4:func.7">exp</a> <font color="Olive" title="b3">z2</font> <a href="lopban_4.html#R1" title="LOPBAN_4:pred.1">are_commutative</a>  )</div></div>
