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<b>set </b><font color="Maroon">VV</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>;<br/>
<b>set </b><font color="Maroon">VW1</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W1</font>;<br/>
<b>set </b><font color="Maroon">VW2</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W2</font>;<br/>
<a NAME="E1:2_1_1"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W1</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W2</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font> )
 
<b>by </b><i><a class="ref" href="rmod_2.html#D2">RMOD_2:def 2</a></i>;<br/>
<a NAME="E2:2_1_1"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W2</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T27">XBOOLE_1:27</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">V1</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W1</font>, <font color="Maroon">V2</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W2</font>, <font color="Maroon">V3</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W2</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font> <b>by </b><i><a class="ref" href="rmod_2.html#D2">RMOD_2:def 2</a></i>;<br/>
<a NAME="E4:2_1_1"/>
(  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W1</font> &amp;  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W2</font> )
 
<b>by </b><i><a class="ref" href="rmod_2.html#T25">RMOD_2:25</a></i>;<br/>
<a NAME="E5:2_1_1"/><b>then </b>
(  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W1</font> &amp;  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W2</font> )
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E6:2_1_1"/><b>then </b><i><font color="Green">E30</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E7:2_1_1"/>
( <font color="Maroon">V1</font> is <a href="rmod_2.html#V1">lineary-closed</a> &amp; <font color="Maroon">V2</font> is <a href="rmod_2.html#V1">lineary-closed</a> )
 
<b>by </b><i><a class="ref" href="rmod_2.html#T41">RMOD_2:41</a></i>;<br/>
<a NAME="E8:2_1_1"/><b>then </b>
<font color="Maroon">V3</font> is <a href="rmod_2.html#V1">lineary-closed</a>
 
<b>by </b><i><a class="ref" href="rmod_2.html#T10">RMOD_2:10</a></i>;<br/>
<b>hence </b><a NAME="E9:2_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being <a href="vectsp_2.html#V3">strict</a>  <a href="rmod_2.html#M1">Submodule</a> of <font color="Maroon">V</font> st the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W2</font>
 <b>by </b><i>, <a class="ref" href="rmod_2.html#T42">RMOD_2:42</a></i>;<br/>


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