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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>, <font color="Maroon">c<sub>3</sub></font> be  <a href="matrlin.html#V2">finite-dimensional</a> <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:28"/><i><font color="Green">E28</font></i>: 
 <a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<a NAME="E2:28"/>
 <a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">c<sub>2</sub></font> is    <a href="vectsp_4.html#M1">Subspace</a> of  <a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="pencil_4.html#E1:28"><i><font color="Green">E28</font></i></a>, <a class="ref" href="vectsp_4.html#T32">VECTSP_4:32</a></i>;<br/>
<a NAME="E3:28"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is    <a href="vectsp_4.html#M1">Subspace</a> of  <a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="pencil_4.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E4:28"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is    <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="pencil_4.html#T4" target="_self">Th4</a></i>;<br/>
<b>hence </b><a NAME="E5:28"/>
<font color="Maroon">c<sub>4</sub></font> <a href="vectsp_9.html#K2">Subspaces_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> <a href="vectsp_9.html#K2">Subspaces_of</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="vectsp_9.html#T42">VECTSP_9:42</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<a NAME="E6:28"/>
 <a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">c<sub>3</sub></font> is    <a href="vectsp_4.html#M1">Subspace</a> of  <a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="pencil_4.html#E1:28"><i><font color="Green">E28</font></i></a>, <a class="ref" href="vectsp_4.html#T32">VECTSP_4:32</a></i>;<br/>
<a NAME="E7:28"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> is    <a href="vectsp_4.html#M1">Subspace</a> of  <a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="pencil_4.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E8:28"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> is    <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="pencil_4.html#T4" target="_self">Th4</a></i>;<br/>
<b>hence </b><a NAME="E9:28"/>
<font color="Maroon">c<sub>4</sub></font> <a href="vectsp_9.html#K2">Subspaces_of</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> <a href="vectsp_9.html#K2">Subspaces_of</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="vectsp_9.html#T42">VECTSP_9:42</a></i>;<br/>


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