<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">RD</font> be   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c1">D</font>;<br/><b>let </b><font color="Maroon" title="c3">F</font>, <font color="Maroon" title="c4">G</font> be    <a href="filter_1.html#M2" title="FILTER_1:mode.2">BinOp</a> of <font color="Maroon" title="c1">D</font>,<font color="Maroon" title="c2">RD</font>;<br/>







<b>assume </b><a NAME="E1:19"/>
( <font color="Maroon" title="c3">F</font> <a href="binop_1.html#R4" title="BINOP_1:pred.4">is_left_distributive_wrt</a> <font color="Maroon" title="c4">G</font> &amp; <font color="Maroon" title="c3">F</font> <a href="binop_1.html#R5" title="BINOP_1:pred.5">is_right_distributive_wrt</a> <font color="Maroon" title="c4">G</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="binop_1.html#D11" title="BINOP_1:def.11">BINOP_1:def 11</a><br/>

<b>hence </b><a NAME="E2:19"/>
( <font color="Maroon" title="c3">F</font> <a href="filter_1.html#K3" title="FILTER_1:func.3">/\/</a> <font color="Maroon" title="c2">RD</font> <a href="binop_1.html#R4" title="BINOP_1:pred.4">is_left_distributive_wrt</a> <font color="Maroon" title="c4">G</font> <a href="filter_1.html#K3" title="FILTER_1:func.3">/\/</a> <font color="Maroon" title="c2">RD</font> &amp; <font color="Maroon" title="c3">F</font> <a href="filter_1.html#K3" title="FILTER_1:func.3">/\/</a> <font color="Maroon" title="c2">RD</font> <a href="binop_1.html#R5" title="BINOP_1:pred.5">is_right_distributive_wrt</a> <font color="Maroon" title="c4">G</font> <a href="filter_1.html#K3" title="FILTER_1:func.3">/\/</a> <font color="Maroon" title="c2">RD</font> )
 <b>by </b><i><a class="ref" href="filter_1.html#T9" target="_self" title="FILTER_1:th.9">Th9</a>, <a class="ref" href="filter_1.html#T10" target="_self" title="FILTER_1:th.10">Th10</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="binop_1.html#D11" title="BINOP_1:def.11">BINOP_1:def 11</a><br/>


</div>
