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<b>let </b><font color="Maroon">K</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V3">Abelian</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="group_1.html#V4">associative</a> <a href="vectsp_1.html#V7">distributive</a> <a href="vectsp_1.html#V8">left_unital</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">V</font> be   <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">S</font> be    <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">V</font>, <font color="Maroon">T</font> be    <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:14"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">S</font> <a href="vectsp_5.html#K2">/\</a> <font color="Maroon">T</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">V</font>
 <b>and </b><br/><a NAME="E2:14"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">S</font>
 <b>and </b><br/><a NAME="E3:14"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">T</font>
 ;<br/>

<a NAME="E4:14"/>
( <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> &amp; <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> )
 
<b>by </b><i>, , <a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E5:14"/><b>then </b>
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E6:14"/><b>then </b>
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="vectsp_5.html#K2">/\</a> <font color="Maroon">T</font></span>)</span>
 
<b>by </b><i><a class="ref" href="vectsp_5.html#D2">VECTSP_5:def 2</a></i>;<br/>
<a NAME="E7:14"/><b>then </b>
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, <a class="ref" href="vectsp_4.html#D3">VECTSP_4:def 3</a></i>;<br/>
<b>hence </b><a NAME="E8:14"/>
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


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