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<span class="kw">set </span><font color="Maroon" title="c3">A</font> =  the    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">VS</font>;<br/>
<a NAME="E1:3_1_1"/>
 for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"> the    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">VS</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">B</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"> the    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">VS</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> <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_8.html#D2" target="_self" onmouseover="rs('vectsp_8/D2')" onmouseout="rh()">Def2</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">B</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c4">B</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/>

<span class="kw">thus </span><a NAME="E3:3_1_1"/>
 not <font color="Maroon" title="c4">B</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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