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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> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<a NAME="E1:21"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E2:21"/><b>then </b>
(  <a href="vectsp_7.html#K1" target="_self">Lin</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is    <a href="vectsp_4.html#M1">Subspace</a> of  <a href="vectsp_7.html#K1" target="_self">Lin</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="vectsp_7.html#K1" target="_self">Lin</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is    <a href="vectsp_4.html#M1">Subspace</a> of  <a href="vectsp_7.html#K1" target="_self">Lin</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="vectsp_7.html#T18" target="_self">Th18</a></i>;<br/>
<b>hence </b><a NAME="E3:21"/>
 <a href="vectsp_7.html#K1" target="_self">Lin</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is    <a href="vectsp_4.html#M1">Subspace</a> of <span class="p1">(<span class="default"><a href="vectsp_7.html#K1" target="_self">Lin</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="vectsp_5.html#K2">/\</a> <span class="p1">(<span class="default"><a href="vectsp_7.html#K1" target="_self">Lin</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_5.html#T24">VECTSP_5:24</a></i>;<br/>


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