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<b>let </b><font color="Maroon" title="c1">X</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="bspace.html#K9" title="BSPACE:func.9">singletons</a> <font color="Maroon" title="c1">X</font> is    <a href="vectsp_7.html#M1" title="VECTSP_7:mode.1">Basis</a> of  <a href="bspace.html#K7" title="BSPACE:func.7">bspace</a> <font color="Maroon" title="c1">X</font></span><br/>

<a NAME="E1:49"/><i><font color="Green" title="E37">A1</font></i>: 
 <a href="bspace.html#K9" title="BSPACE:func.9">singletons</a> <font color="Maroon" title="c1">X</font> is <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>
 
<b>by </b><i><a class="ref" href="bspace.html#T37" target="_self" title="BSPACE:th.37">Th37</a></i>;<br/>
<a NAME="E2:49"/>
 <a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <span class="p1">(<span class="default"><a href="bspace.html#K9" title="BSPACE:func.9">singletons</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bspace.html#K7" title="BSPACE:func.7">bspace</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="bspace.html#T40" target="_self" title="BSPACE:th.40">Th40</a></i>;<br/>
<b>hence </b><a NAME="E3:49"/>
 <a href="bspace.html#K9" title="BSPACE:func.9">singletons</a> <font color="Maroon" title="c1">X</font> is    <a href="vectsp_7.html#M1" title="VECTSP_7:mode.1">Basis</a> of  <a href="bspace.html#K7" title="BSPACE:func.7">bspace</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="txt" href="bspace.html#E1:49"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="vectsp_7.html#D3" title="VECTSP_7:def.3">VECTSP_7:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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