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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="rlsub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:25"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is    <a href="rlsub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> is    <a href="rlsub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:25_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:25_1"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="rlvect_3.html#E1:25"><i><font color="Green">E19</font></i></a>, <a class="ref" href="rlsub_1.html#T16">RLSUB_1:16</a></i>;<br/><b>hence </b><a NAME="E3:25_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="rlsub_2.html#K2">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="rlsub_2.html#T7">RLSUB_2:7</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:25"/>
<font color="Maroon">c<sub>2</sub></font> is    <a href="rlsub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>3</sub></font> <a href="rlsub_2.html#K2">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="rlsub_1.html#T37">RLSUB_1:37</a></i>;<br/>


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