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<b>let </b><font color="Maroon">X</font> be   <a href="clopban2.html#NM3">Complex_Banach_Algebra</a>;<br/><b>let </b><font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>;<br/>



<font color="Maroon">z</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">z</font></span>)</span> = 
<font color="Maroon">z</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="clvect_1.html#K1">*</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="clopban3.html#T42">CLOPBAN3:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="clvect_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="group_1.html#K1">*</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="clopban3.html#T42">CLOPBAN3:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="clvect_1.html#K1">*</a> <font color="Maroon">z</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">z</font>
<b>by </b><i><a class="ref" href="clopban3.html#T42">CLOPBAN3:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">z</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">z</font>
<b>by </b><i><a class="ref" href="clopban3.html#T42">CLOPBAN3:42</a></i>
;<br/>
<a NAME="E2:50"/><b>then </b><i><font color="Green">E51</font></i>: 
<font color="Maroon">z</font>, <a href="rlvect_1.html#K5">-</a> <font color="Maroon">z</font> <a href="clopban4.html#R1" target="_self">are_commutative</a> 
 
<b>by </b><i/>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="clopban4.html#K8" target="_self">exp</a> <font color="Maroon">z</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><a href="clopban4.html#K8" target="_self">exp</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">z</font></span>)</span></span>)</span> = 
 <a href="clopban4.html#K8" target="_self">exp</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">z</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="clopban4.html#D1" target="_self">Def1</a>, </i>
<br/>.= 
 <a href="clopban4.html#K8" target="_self">exp</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">X</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T16">RLVECT_1:16</a></i>
<br/>.= 
 <a href="group_1.html#K2">1.</a> <font color="Maroon">X</font>
<b>by </b><i/>
;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="clopban4.html#K8" target="_self">exp</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><a href="clopban4.html#K8" target="_self">exp</a> <font color="Maroon">z</font></span>)</span> = 
 <a href="clopban4.html#K8" target="_self">exp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">z</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="clopban4.html#D1" target="_self">Def1</a>, </i>
<br/>.= 
 <a href="clopban4.html#K8" target="_self">exp</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">X</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T16">RLVECT_1:16</a></i>
<br/>.= 
 <a href="group_1.html#K2">1.</a> <font color="Maroon">X</font>
<b>by </b><i/>
;<br/>


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