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<b>let </b><font color="Maroon">A</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">o</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">A</font>, <font color="Maroon">o'</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">A</font>;<br/>



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( <font color="Maroon">o'</font> <a href="binop_1.html#R5" target="_self">is_right_distributive_wrt</a> <font color="Maroon">o</font> iff for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font> holds  <font color="Maroon">o'</font> <a href="binop_1.html#K2" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">o</font> <a href="binop_1.html#K2" target="_self">.</a> <font color="Olive">a</font>,<font color="Olive">b</font></span>)</span>,<font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font> <a href="binop_1.html#K2" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">o'</font> <a href="binop_1.html#K2" target="_self">.</a> <font color="Olive">a</font>,<font color="Olive">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">o'</font> <a href="binop_1.html#K2" target="_self">.</a> <font color="Olive">b</font>,<font color="Olive">c</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:29"/>
( <font color="Maroon">o'</font> is <a href="binop_1.html#V1" target="_self">commutative</a> implies ( <font color="Maroon">o'</font> <a href="binop_1.html#R6" target="_self">is_distributive_wrt</a> <font color="Maroon">o</font> iff <font color="Maroon">o'</font> <a href="binop_1.html#R5" target="_self">is_right_distributive_wrt</a> <font color="Maroon">o</font> ) )
 <b>by </b><i/>;<br/>


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