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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:19"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="binop_1.html#V1" target="_self">commutative</a>
 ;<br/>

<a NAME="E2:19"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#R3" target="_self">is_a_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font> iff <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#R1" target="_self">is_a_left_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="binop_1.html#T14" target="_self">Th14</a></i>;<br/>
<b>hence </b><a NAME="E3:19"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#R1" target="_self">is_a_left_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font> iff <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#R2" target="_self">is_a_right_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="binop_1.html#E1:19"><i><font color="Green">E12</font></i></a>, <a class="ref" href="binop_1.html#T15" target="_self">Th15</a></i>;<br/>


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