<?xml version="1.0"?>
<div class="add">

<b>reconsider </b><font color="Maroon" title="c2">G</font> =  <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ,<a href="binop_2.html#K33" title="BINOP_2:func.33">addreal</a>  #) as   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a> <b>by </b><i><a class="ref" href="group_1.html#T7" target="_self" title="GROUP_1:th.7">Th7</a></i>;<br/>
<a NAME="E2:86"/>
<font color="Maroon" title="c2">G</font> is <a href="group_1.html#V7" title="GROUP_1:attr.7">commutative</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="86_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">h</font>, <font color="Maroon" title="c4">g</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="group_1.html#D16" target="_self" title="GROUP_1:def.16">GROUP_1:def 16</a><br/>

<b>reconsider </b><font color="Maroon" title="c5">A</font> = <font color="Maroon" title="c3">h</font>, <font color="Maroon" title="c6">B</font> = <font color="Maroon" title="c4">g</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/>
<b>thus </b><font color="Maroon" title="c3">h</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c4">g</font> = 
<font color="Maroon" title="c6">B</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <font color="Maroon" title="c5">A</font>
<b>by </b><i><a class="ref" href="binop_2.html#D9" title="BINOP_2:def.9">BINOP_2:def 9</a></i>
<br/>.= 
<font color="Maroon" title="c4">g</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c3">h</font>
<b>by </b><i><a class="ref" href="binop_2.html#D9" title="BINOP_2:def.9">BINOP_2:def 9</a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:86"/>
 <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ,<a href="binop_2.html#K33" title="BINOP_2:func.33">addreal</a>  #) is  <a href="group_1.html#V7" title="GROUP_1:attr.7">commutative</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>
 ;<br/>


</div>
