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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="vectsp_6.html#M1">Linear_Combination</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:13"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>6</sub></font> is <a href="vectsp_7.html#V1">linearly-independent</a>
 <b>and </b><br/><a NAME="E2:13"/><i><font color="Green">E10</font></i>: 
 <a href="vectsp_6.html#K1">Carrier</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E3:13"/><i><font color="Green">E11</font></i>: 
 <a href="vectsp_6.html#K1">Carrier</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E4:13"/><i><font color="Green">E12</font></i>: 
 <a href="vectsp_6.html#K1">Carrier</a> <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E5:13"/><i><font color="Green">E13</font></i>: 
 <a href="vectsp_6.html#K4">Sum</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K4">Sum</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K4">Sum</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 ;<br/>

<a NAME="E6:13"/><i><font color="Green">E14</font></i>: 
 <a href="vectsp_6.html#K1">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="vectsp_6.html#K5">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K1">Carrier</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K1">Carrier</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="vectsp_6.html#T51">VECTSP_6:51</a></i>;<br/>
<a NAME="E7:13"/>
<span class="p1">(<span class="default"><a href="vectsp_6.html#K1">Carrier</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K1">Carrier</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="matrlin.html#E3:13"><i><font color="Green">E11</font></i></a>, <a class="txt" href="matrlin.html#E4:13"><i><font color="Green">E12</font></i></a>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E8:13"/><b>then </b><i><font color="Green">E15</font></i>: 
 <a href="vectsp_6.html#K1">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="vectsp_6.html#K5">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="matrlin.html#E6:13"><i><font color="Green">E14</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E9:13"/>
 <a href="vectsp_6.html#K4">Sum</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="vectsp_6.html#K4">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="vectsp_6.html#K5">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="matrlin.html#E5:13"><i><font color="Green">E13</font></i></a>, <a class="ref" href="vectsp_6.html#T77">VECTSP_6:77</a></i>;<br/>
<b>hence </b><a NAME="E10:13"/>
<font color="Maroon">c<sub>3</sub></font> <a href="vectsp_6.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="vectsp_6.html#K5">+</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="matrlin.html#E1:13"><i><font color="Green">E9</font></i></a>, <a class="txt" href="matrlin.html#E2:13"><i><font color="Green">E10</font></i></a>, <a class="txt" href="matrlin.html#E8:13"><i><font color="Green">E15</font></i></a>, <a class="ref" href="matrlin.html#T9" target="_self">Th9</a></i>;<br/>


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