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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font>;<br/>



<b>assume </b><a NAME="E1:22"/>
<font color="Maroon" title="c2">A</font> is <a href="rlvect_3.html#V1" title="RLVECT_3:attr.1">linearly-independent</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c3">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E3:22"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B</font>
 <b>and </b><br/><a NAME="E4:22"/><i><font color="Green" title="E16">A2</font></i>: 
( <font color="Maroon" title="c3">B</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="c3">B</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 <font color="Maroon" title="c1">V</font>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">U2</a> of <font color="Maroon" title="c1">V</font>,the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c1">V</font>,the <a href="rlvect_1.html#U2" title="RLVECT_1:sel.2">Mult</a> of <font color="Maroon" title="c1">V</font>,the <a href="bhsp_1.html#U1" title="BHSP_1:sel.1">scalar</a> of <font color="Maroon" title="c1">V</font> #) )
 <b>by </b><i><a class="ref" href="rusub_3.html#T11" target="_self" title="RUSUB_3:th.11">Th11</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">B</font> = <font color="Maroon" title="c3">B</font> as    <a href="rusub_3.html#M1" title="RUSUB_3:mode.1">Basis</a> of <font color="Maroon" title="c1">V</font> <b>by </b><i><a class="txt" href="rusub_3.html#E4:22"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="rusub_3.html#D2" target="_self" title="RUSUB_3:def.2">Def2</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">B</font>
;<br/>

<b>thus </b><a NAME="E6:22"/>
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font>
 <b>by </b><i><a class="txt" href="rusub_3.html#E3:22"><i><font color="Green" title="E15">A1</font></i></a></i>;<br/>


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