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<span class="kw">let </span><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">V</font> being  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">F</font>  st  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Olive" title="b1">V</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  holds <br/><font color="Olive" title="b1">V</font> is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">F</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">V</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  implies <font color="Maroon" title="c2">V</font> is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  )</span><br/>



<span class="kw">consider </span><font color="Maroon" title="c3">B</font> being    <a href="vectsp_7.html#M1" title="VECTSP_7:mode.1">Basis</a> of <font color="Maroon" title="c2">V</font>;<br/>
<span class="kw">assume </span><a NAME="E2:6"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">V</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">V</font> is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a> </span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">B</font> = <font color="Maroon" title="c3">B</font> as   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">B</font>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="matrlin.html#D3" title="MATRLIN:def.3">MATRLIN:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">B</font> is    <a href="vectsp_7.html#M1" title="VECTSP_7:mode.1">Basis</a> of <font color="Maroon" title="c2">V</font></span><br/>

<span class="kw">thus </span><a NAME="E4:6"/>
<font color="Maroon" title="c4">B</font> is    <a href="vectsp_7.html#M1" title="VECTSP_7:mode.1">Basis</a> of <font color="Maroon" title="c2">V</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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