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<b>let </b><font color="Maroon" title="c2">L</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a> ;<br/>

<b>assume </b><a NAME="E1:27"/><i><font color="Green" title="E10">A1</font></i>: 
<font color="Maroon" title="c2">L</font> is <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">distributive</a>
 ;<br/>

<a NAME="E2:27"/><b>then </b>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> holds  <font color="Olive" title="b1">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Olive" title="b3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Olive" title="b3">c</font></span>)</span>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D18" target="_self" title="VECTSP_1:def.18">Def18</a></i>;<br/>
<b>hence </b><a NAME="E3:27"/>
<font color="Maroon" title="c2">L</font> is <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">right-distributive</a>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D11" target="_self" title="VECTSP_1:def.11">Def11</a></i>;<br/>

<a NAME="E4:27"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Olive" title="b3">c</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">c</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Olive" title="b1">a</font></span>)</span>
 
<b>by </b><i><a class="txt" href="vectsp_1.html#E1:27"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="vectsp_1.html#D18" target="_self" title="VECTSP_1:def.18">Def18</a></i>;<br/>
<b>hence </b><a NAME="E5:27"/>
<font color="Maroon" title="c2">L</font> is <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">left-distributive</a>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D12" target="_self" title="VECTSP_1:def.12">Def12</a></i>;<br/>


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