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<a NAME="E1:8_1_1"/>
(  <a href="group_1.html#G1" target="_self">HGrStr</a>(# <a href="numbers.html#K1">REAL</a> ,<a href="binop_2.html#K33">addreal</a>  #) is <a href="group_1.html#V3" target="_self">Group-like</a> &amp;  <a href="group_1.html#G1" target="_self">HGrStr</a>(# <a href="numbers.html#K1">REAL</a> ,<a href="binop_2.html#K33">addreal</a>  #) is <a href="group_1.html#V4" target="_self">associative</a> )
 
<b>by </b><i><a class="ref" href="group_1.html#D3" target="_self">Def3</a>, <a class="ref" href="group_1.html#D4" target="_self">Def4</a>, <a class="txt" href="group_1.html#E2"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:8_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being non <a href="struct_0.html#V3">empty</a>  <a href="group_1.html#L1" target="_self">HGrStr</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="group_1.html#V1" target="_self">strict</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="group_1.html#V3" target="_self">Group-like</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="group_1.html#V4" target="_self">associative</a> )
 ;<br/>


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