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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="clopban2.html#NM3" title="CLOPBAN2:NM.3">Complex_Banach_Algebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">s</font>, <font color="Olive" title="b3">t</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a> holds  <font color="Olive" title="b2">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b1">z</font>,<font color="Olive" title="b3">t</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b1">z</font> <a href="lopban_4.html#R1" title="LOPBAN_4:pred.1">are_commutative</a> </span><br/><b>let </b><font color="Maroon" title="c2">z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">t</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a> holds  <font color="Olive" title="b1">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">z</font>,<font color="Olive" title="b2">t</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">z</font> <a href="lopban_4.html#R1" title="LOPBAN_4:pred.1">are_commutative</a> </span><br/><b>let </b><font color="Maroon" title="c3">s</font>, <font color="Maroon" title="c4">t</font> be   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c4">t</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">z</font> <a href="lopban_4.html#R1" title="LOPBAN_4:pred.1">are_commutative</a> </span><br/>





<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">t</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">z</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">z</font></span>)</span>
<b>by </b><i><a class="ref" href="clopban3.html#T42" title="CLOPBAN3:th.42">CLOPBAN3:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">t</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">z</font></span>)</span>
<b>by </b><i><a class="ref" href="clopban3.html#T42" title="CLOPBAN3:th.42">CLOPBAN3:42</a></i>
;<br/>
<b>hence </b><a NAME="E2:50"/>
<font color="Maroon" title="c3">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c4">t</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">z</font> <a href="lopban_4.html#R1" title="LOPBAN_4:pred.1">are_commutative</a> 
 <b>by </b><i><a class="ref" href="lopban_4.html#D1" title="LOPBAN_4:def.1">LOPBAN_4:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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