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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="vectsp_1.html#V4">right-distributive</a> <a href="vectsp_1.html#V6">right_unital</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">I</font> be   <a href="ideal_1.html#NM2">RightIdeal</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>





<b>assume </b><a NAME="E1:31"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> )
 ;<br/>

<a NAME="E2:31"/><b>then </b>
 <a href="rlvect_1.html#K5">-</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:31"/><b>then </b>
<font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">y</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:31"/>
<font color="Maroon">x</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D11">RLVECT_1:def 11</a></i>;<br/>


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