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<span class="kw">set </span><font color="Maroon" title="c2">V</font> =  the   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font>;<br/>
<span class="kw">take </span>
 <a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a>  the   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a>  the   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font> is  <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>  &amp;  <a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a>  the   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font> is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E1:12_1_1"/>
 <a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a>  the   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font> is  <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a>  the   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font> is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a> </span><br/>

<span class="kw">take </span><font color="Maroon" title="c3">A</font> =  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a>  the   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font></span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="matrlin.html#D1" target="_self" title="MATRLIN:def.1">MATRLIN:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">A</font> is    <a href="vectsp_7.html#M1" title="VECTSP_7:mode.1">Basis</a> of  <a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a>  the   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font></span><br/>

<a NAME="E2:12_1_1"/>
 <a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a> <span class="p1">(<span class="default"><a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a>  the   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_7.html#T9" title="VECTSP_7:th.9">VECTSP_7:9</a></span>;<br/>
<a NAME="E3:12_1_1"/><span class="kw">then </span>
 <a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_1.html#G1" title="VECTSP_1:aggr.1">VectSpStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a>  the   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font></span>)</span>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <span class="p1">(<span class="default"><a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a>  the   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font></span>)</span>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <span class="p1">(<span class="default"><a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a>  the   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font></span>)</span>, the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">lmult</a> of <span class="p1">(<span class="default"><a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a>  the   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font></span>)</span> #)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_4.html#T36" title="VECTSP_4:th.36">VECTSP_4:36</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:12_1_1"/>
<font color="Maroon" title="c3">A</font> is    <a href="vectsp_7.html#M1" title="VECTSP_7:mode.1">Basis</a> of  <a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a>  the   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_7.html#D3" title="VECTSP_7:def.3">VECTSP_7:def 3</a></span>; <a class="txt" 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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