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<b>let </b><font color="Maroon">X</font> be   <a href="lopban_2.html#NM3">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/><b>let </b><font color="Maroon">s</font> be   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">t</font> be   <a href="real_1.html#NM1">Real</a>;<br/>





<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">z</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">z</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="real_1.html#K4">*</a> <font color="Maroon">t</font></span>)</span> <a href="rlvect_1.html#K3">*</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="lopban_3.html#T43">LOPBAN_3:43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">z</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="lopban_3.html#T43">LOPBAN_3:43</a></i>
;<br/>
<b>hence </b><a NAME="E2:55"/>
<font color="Maroon">s</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">z</font>,<font color="Maroon">t</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">z</font> <a href="lopban_4.html#R1" target="_self">are_commutative</a> 
 <b>by </b><i/>;<br/>


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