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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="rlvect_2.html#M1">Linear_Combination</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:24"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>and </b><br/><a NAME="E3:24"/><i><font color="Green">E16</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_2.html#K3">Carrier</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E4:24"/><i><font color="Green">E17</font></i>: 
 <a href="rlvect_2.html#K6">Sum</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_2.html#K5">(#)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="rlvect_2.html#D10">RLVECT_2:def 10</a></i>;<br/>
<b>assume </b><a NAME="E5:24"/>
 <a href="rlvect_2.html#K3">Carrier</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_3.html#K1" target="_self">Lin</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="rlvect_2.html#M2">Linear_Combination</a> of <font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E7:24"/><i><font color="Green">E18</font></i>: 
 <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_2.html#K5">(#)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_2.html#K6">Sum</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="rusub_3.html#E3:24"><i><font color="Green">E16</font></i></a>, <a class="ref" href="rusub_3.html#T16" target="_self">Th16</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E8:24"/>
 <a href="rlvect_2.html#K6">Sum</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_2.html#K6">Sum</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="rusub_3.html#E4:24"><i><font color="Green">E17</font></i></a>, <a class="txt" href="rusub_3.html#E7:24"><i><font color="Green">E18</font></i></a></i>;<br/>


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