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<b>let </b><font color="Maroon" title="c1">A</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">o</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">A</font>;<br/><b>let </b><font color="Maroon" title="c3">e</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font>;<br/>





<a NAME="E1:17"/>
( <font color="Maroon" title="c3">e</font> <a href="binop_1.html#R1" title="BINOP_1:pred.1">is_a_left_unity_wrt</a> <font color="Maroon" title="c2">o</font> iff for <font color="Olive" title="b1">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c2">o</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">e</font>,<font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> )
 
<b>by </b><i><a class="ref" href="binop_1.html#D5" target="_self" title="BINOP_1:def.5">Def5</a></i>;<br/>
<b>hence </b><a NAME="E2:17"/>
( <font color="Maroon" title="c2">o</font> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> implies ( <font color="Maroon" title="c3">e</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon" title="c2">o</font> iff <font color="Maroon" title="c3">e</font> <a href="binop_1.html#R1" title="BINOP_1:pred.1">is_a_left_unity_wrt</a> <font color="Maroon" title="c2">o</font> ) )
 <b>by </b><i><a class="ref" href="binop_1.html#T12" target="_self" title="BINOP_1:th.12">Th12</a></i>;<br/>


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