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<span class="kw">reconsider </span><font color="Maroon" title="c1">G</font> =  <a href="algstr_0.html#G1" title="ALGSTR_0:aggr.1">addMagma</a>(# <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="binop_2.html#K9" title="BINOP_2:func.9">addreal</a> #) as   <a href="group_1a.html#NM1" title="GROUP_1A:NM.1">addGroup</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_1a.html#T3" target="_self" onmouseover="rs('group_1a/T3')" onmouseout="rh()">Th3</a></span>;<br/>
<a NAME="E2:66"/>
<font color="Maroon" title="c1">G</font> is  <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a> 
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="66_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">h</font>, <font color="Maroon" title="c3">g</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="rlvect_1.html#D2" onmouseover="rs('rlvect_1/D2')" onmouseout="rh()">RLVECT_1:def 2</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">h</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c2">h</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c4">A</font> = <font color="Maroon" title="c2">h</font>, <font color="Maroon" title="c5">B</font> = <font color="Maroon" title="c3">g</font> as   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> ;<br/>
<span class="kw">thus </span><font color="Maroon" title="c2">h</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c3">g</font> = 
<font color="Maroon" title="c5">B</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">A</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binop_2.html#D9" onmouseover="rs('binop_2/D9')" onmouseout="rh()">BINOP_2:def 9</a></span>
<br/>.= 
<font color="Maroon" title="c3">g</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c2">h</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binop_2.html#D9" onmouseover="rs('binop_2/D9')" onmouseout="rh()">BINOP_2:def 9</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:66"/>
 <a href="algstr_0.html#G1" title="ALGSTR_0:aggr.1">addMagma</a>(# <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="binop_2.html#K9" title="BINOP_2:func.9">addreal</a> #) is   <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>  <a href="group_1a.html#NM1" title="GROUP_1A:NM.1">addGroup</a>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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