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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="lopban_2.html#NM3">Banach_Algebra</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:54"/><i><font color="Green">E51</font></i>: 
( <span class="p1">(<span class="default"><a href="lopban_4.html#K10" target="_self">exp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><a href="lopban_4.html#K10" target="_self">exp</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="lopban_4.html#K10" target="_self">exp</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><a href="lopban_4.html#K10" target="_self">exp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="lopban_4.html#T38" target="_self">Th38</a></i>;<br/>
<b>hence </b><a NAME="E2:54"/>
 <a href="lopban_4.html#K10" target="_self">exp</a> <font color="Maroon">c<sub>2</sub></font> is <a href="lopban_3.html#V4">invertible</a>
 <b>by </b><i><a class="ref" href="lopban_3.html#D8">LOPBAN_3:def 8</a></i>;<br/>

<b>hence </b><a NAME="E3:54"/>
<span class="p1">(<span class="default"><a href="lopban_4.html#K10" target="_self">exp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lopban_3.html#K9">"</a>  <a href="hidden.html#R1">=</a>  <a href="lopban_4.html#K10" target="_self">exp</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="lopban_4.html#E1:54"><i><font color="Green">E51</font></i></a>, <a class="ref" href="lopban_3.html#D12">LOPBAN_3:def 12</a></i>;<br/>

<b>thus </b><a NAME="E4:54"/>
 <a href="lopban_4.html#K10" target="_self">exp</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="lopban_3.html#V4">invertible</a>
 <b>by </b><i><a class="txt" href="lopban_4.html#E1:54"><i><font color="Green">E51</font></i></a>, <a class="ref" href="lopban_3.html#D8">LOPBAN_3:def 8</a></i>;<br/>

<b>hence </b><a NAME="E5:54"/>
<span class="p1">(<span class="default"><a href="lopban_4.html#K10" target="_self">exp</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="lopban_3.html#K9">"</a>  <a href="hidden.html#R1">=</a>  <a href="lopban_4.html#K10" target="_self">exp</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="lopban_4.html#E1:54"><i><font color="Green">E51</font></i></a>, <a class="ref" href="lopban_3.html#D12">LOPBAN_3:def 12</a></i>;<br/>


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