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

<b>let </b><font color="Maroon">D1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">D2</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:71_1_2"/><i><font color="Green">E52</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D1</font> iff <font color="Olive">x</font> is    <a href="rlvect_2.html#M1" target="_self">Linear_Combination</a> of <font color="Maroon">V</font> )
 ;<br/>

<b>assume </b><a NAME="E2:71_1_2"/><i><font color="Green">E53</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D2</font> iff <font color="Olive">x</font> is    <a href="rlvect_2.html#M1" target="_self">Linear_Combination</a> of <font color="Maroon">V</font> )
 ;<br/>

<b>thus </b><a NAME="E3:71_1_2"/>
<font color="Maroon">D1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D2</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:71_1_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D1</font>
 ;<br/>

<a NAME="E2:71_1_2_1"/><b>then </b>
<font color="Maroon">x</font> is    <a href="rlvect_2.html#M1" target="_self">Linear_Combination</a> of <font color="Maroon">V</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:71_1_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D2</font>
 <b>by </b><i><a class="ref" href="rlvect_2.html#D1" target="_self">Def1</a></i>;<br/>


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

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E4:71_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D2</font>
 ;<br/>

<a NAME="E5:71_1_2"/><b>then </b>
<font color="Maroon">x</font> is    <a href="rlvect_2.html#M1" target="_self">Linear_Combination</a> of <font color="Maroon">V</font>
 
<b>by </b><i><a class="ref" href="rlvect_2.html#D1" target="_self">Def1</a></i>;<br/>
<b>hence </b><a NAME="E6:71_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D1</font>
 <b>by </b><i/>;<br/>


</div>
