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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="filter_1.html#M2" target="_self">BinOp</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><a NAME="E1:19"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#R4">is_left_distributive_wrt</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#R5">is_right_distributive_wrt</a> <font color="Maroon">c<sub>4</sub></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="E2:19"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="filter_1.html#K3" target="_self">/\/</a> <font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#R4">is_left_distributive_wrt</a> <font color="Maroon">c<sub>4</sub></font> <a href="filter_1.html#K3" target="_self">/\/</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="filter_1.html#K3" target="_self">/\/</a> <font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#R5">is_right_distributive_wrt</a> <font color="Maroon">c<sub>4</sub></font> <a href="filter_1.html#K3" target="_self">/\/</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="filter_1.html#T9" target="_self">Th9</a>, <a class="ref" href="filter_1.html#T10" target="_self">Th10</a></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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