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<span class="kw">consider </span><font color="Maroon" title="c1">V</font> being   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a>;<br/>
<span class="kw">take </span>
 <a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font> is  <a href="bhsp_1.html#V1" title="BHSP_1:attr.1">strict</a>  &amp;  <a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font> is  <a href="rusub_4.html#V1" title="RUSUB_4:attr.1">finite-dimensional</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E2:6_1_1"/>
 <a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font> is  <a href="bhsp_1.html#V1" title="BHSP_1:attr.1">strict</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font> is  <a href="rusub_4.html#V1" title="RUSUB_4:attr.1">finite-dimensional</a> </span><br/>

<span class="kw">take </span><font color="Maroon" title="c2">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="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font></span>)</span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="rusub_4.html#D1" target="_self" title="RUSUB_4:def.1">RUSUB_4:def 1</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">A</font> is    <a href="rusub_3.html#M1" title="RUSUB_3:mode.1">Basis</a> of  <a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font></span><br/>

<a NAME="E3:6_1_1"/>
 <a href="rusub_3.html#K1" title="RUSUB_3:func.1">Lin</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <span class="p1">(<span class="default"><a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rusub_3.html#T3" title="RUSUB_3:th.3">RUSUB_3:3</a></span>;<br/>
<a NAME="E4:6_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c2">A</font> is  <a href="rlvect_3.html#V1" title="RLVECT_3:attr.1">linearly-independent</a>  &amp;  <a href="rusub_3.html#K1" title="RUSUB_3:func.1">Lin</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bhsp_1.html#G1" title="BHSP_1:aggr.1">UNITSTR</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</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="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</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="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font></span>)</span>,the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <span class="p1">(<span class="default"><a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font></span>)</span>,the <a href="bhsp_1.html#U1" title="BHSP_1:sel.1">scalar</a> of <span class="p1">(<span class="default"><a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font></span>)</span> #) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_3.html#T8" title="RLVECT_3:th.8">RLVECT_3:8</a>, <a class="ref" href="rusub_1.html#T30" title="RUSUB_1:th.30">RUSUB_1:30</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:6_1_1"/>
<font color="Maroon" title="c2">A</font> is    <a href="rusub_3.html#M1" title="RUSUB_3:mode.1">Basis</a> of  <a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rusub_3.html#D2" title="RUSUB_3:def.2">RUSUB_3:def 2</a></span>; <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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