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

<b>consider </b><font color="Maroon" title="c3">A</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">VS</font>;<br/>
<a NAME="E2:3_1_1"/>
for <font color="Olive" title="b1">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">A</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><font color="Olive" title="b1">X</font> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">VS</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">B</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">A</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> as    <a href="vectsp_8.html#M1" title="VECTSP_8:mode.1">SubVS-Family</a> of <font color="Maroon" title="c2">VS</font> <b>by </b><i><a class="ref" href="vectsp_8.html#D2" target="_self" title="VECTSP_8:def.2">Def2</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">B</font>
;<br/>

<b>thus </b><a NAME="E4:3_1_1"/>
not <font color="Maroon" title="c4">B</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/>


</div>
