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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <font color="Maroon" title="c1">G</font> is <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a></span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <font color="Maroon" title="c1">G</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="group_1.html#D16" title="GROUP_1:def.16">GROUP_1:def 16</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">a</font></span><br/>



<b>reconsider </b><font color="Maroon" title="c4">x</font> = <font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c5">y</font> = <font color="Maroon" title="c3">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="ref" href="group_2.html#T51" title="GROUP_2:th.51">GROUP_2:51</a></i>;<br/>
<a NAME="E2:86"/><i><font color="Green" title="E45">A1</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">b</font> = 
<font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font>
<b>by </b><i><a class="ref" href="group_2.html#T52" title="GROUP_2:th.52">GROUP_2:52</a></i>
<br/>.= 
<font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font>
<b>by </b><i><a class="txt" href="#E2:86"><i><font color="Green" title="E45">A1</font></i></a>, <a class="ref" href="group_5.html#T89" target="_self" title="GROUP_5:th.89">Th89</a></i>
<br/>.= 
<font color="Maroon" title="c3">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">a</font>
<b>by </b><i><a class="ref" href="group_2.html#T52" title="GROUP_2:th.52">GROUP_2:52</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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