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<b>let </b><font color="Maroon">D</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">S</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">f1</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">D</font>, <font color="Maroon">f2</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">g1</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">S</font>, <font color="Maroon">g2</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">S</font>;<br/>







<b>assume </b><a NAME="E1:4"/>
( <font color="Maroon">g1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="realset1.html#K1">||</a> <font color="Maroon">S</font> &amp; <font color="Maroon">g2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="realset1.html#K1">||</a> <font color="Maroon">S</font> &amp; <font color="Maroon">f1</font> <a href="binop_1.html#R4">is_left_distributive_wrt</a> <font color="Maroon">f2</font> &amp; <font color="Maroon">f1</font> <a href="binop_1.html#R5">is_right_distributive_wrt</a> <font color="Maroon">f2</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="binop_1.html#D11">BINOP_1:def 11</a><br/>

<b>hence </b><a NAME="E2:4"/>
( <font color="Maroon">g1</font> <a href="binop_1.html#R4">is_left_distributive_wrt</a> <font color="Maroon">g2</font> &amp; <font color="Maroon">g1</font> <a href="binop_1.html#R5">is_right_distributive_wrt</a> <font color="Maroon">g2</font> )
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="binop_1.html#D11">BINOP_1:def 11</a><br/>


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