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

<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="vectsp_1.html#L3" target="_self">doubleLoopStr</a> ;<br/>

<b>assume </b><a NAME="E1:25"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">L</font> is <a href="vectsp_1.html#V7" target="_self">distributive</a>
 ;<br/>

<a NAME="E2:25"/><b>then </b>
for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds  <font color="Olive">a</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Olive">b</font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">c</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">b</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">c</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:25"/>
<font color="Maroon">L</font> is <a href="vectsp_1.html#V4" target="_self">right-distributive</a>
 <b>by </b><i/>;<br/>

<a NAME="E4:25"/>
for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds  <span class="p1">(<span class="default"><font color="Olive">b</font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">c</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b</font> <a href="group_1.html#K1">*</a> <font color="Olive">a</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">c</font> <a href="group_1.html#K1">*</a> <font color="Olive">a</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:25"/>
<font color="Maroon">L</font> is <a href="vectsp_1.html#V5" target="_self">left-distributive</a>
 <b>by </b><i/>;<br/>


</div>
