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<b>set </b><font color="Maroon" title="c4">VV</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>;<br/>
<b>set </b><font color="Maroon" title="c5">VW1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">W1</font>;<br/>
<b>set </b><font color="Maroon" title="c6">VW2</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W2</font>;<br/>
<a NAME="E1:2_1_1"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">W1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font> )
 
<b>by </b><i><a class="ref" href="rlsub_1.html#D2" title="RLSUB_1:def.2">RLSUB_1:def 2</a></i>;<br/>
<a NAME="E2:2_1_1"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">W1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T27" title="XBOOLE_1:th.27">XBOOLE_1:27</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c7">V1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">W1</font>, <font color="Maroon" title="c8">V2</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W2</font>, <font color="Maroon" title="c9">V3</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">W1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W2</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font> <b>by </b><i><a class="ref" href="rlsub_1.html#D2" title="RLSUB_1:def.2">RLSUB_1:def 2</a></i>;<br/>
<a NAME="E4:2_1_1"/>
(  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">V</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c2">W1</font> &amp;  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">V</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c3">W2</font> )
 
<b>by </b><i><a class="ref" href="rlsub_1.html#T25" title="RLSUB_1:th.25">RLSUB_1:25</a></i>;<br/>
<a NAME="E5:2_1_1"/><b>then </b>
(  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">V</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">W1</font> &amp;  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">V</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W2</font> )
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1" title="RLVECT_1:def.1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E6:2_1_1"/><b>then </b><i><font color="Green" title="E2">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">W1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E7:2_1_1"/>
( <font color="Maroon" title="c7">V1</font> is <a href="rlsub_1.html#V1" title="RLSUB_1:attr.1">lineary-closed</a> &amp; <font color="Maroon" title="c8">V2</font> is <a href="rlsub_1.html#V1" title="RLSUB_1:attr.1">lineary-closed</a> )
 
<b>by </b><i><a class="ref" href="rlsub_1.html#T42" title="RLSUB_1:th.42">RLSUB_1:42</a></i>;<br/>
<a NAME="E8:2_1_1"/><b>then </b>
<font color="Maroon" title="c9">V3</font> is <a href="rlsub_1.html#V1" title="RLSUB_1:attr.1">lineary-closed</a>
 
<b>by </b><i><a class="ref" href="rlsub_1.html#T10" title="RLSUB_1:th.10">RLSUB_1:10</a></i>;<br/>
<b>hence </b><a NAME="E9:2_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">strict</a>  <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c1">V</font> st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">W1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W2</font>
 <b>by </b><i><a class="txt" href="rlsub_2.html#E6:2_1_1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="rlsub_1.html#T43" title="RLSUB_1:th.43">RLSUB_1:43</a></i>;<br/>


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