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<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/>



<b>thus </b><a NAME="E1:19"/>
( <font color="Maroon">x</font> <a href="rlvect_1.html#R1">in</a>  <a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">V</font> implies <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:19_1"/>
<font color="Maroon">x</font> <a href="rlvect_1.html#R1">in</a>  <a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">V</font>
 ;<br/>

<a NAME="E2:19_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E3:19_1"/><b>then </b>
<font color="Maroon">x</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="rlsub_1.html#D3">RLSUB_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E4:19_1"/>
<font color="Maroon">x</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/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:19"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> implies <font color="Maroon">x</font> <a href="rlvect_1.html#R1">in</a>  <a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">V</font> )
 <b>by </b><i><a class="ref" href="rlsub_1.html#T25">RLSUB_1:25</a></i>;<br/>


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