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<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/><b>let </b><font color="Maroon" title="c2">V</font>, <font color="Maroon" title="c3">W</font> be   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">F</font>;<br/>



<b>assume </b><a NAME="E1:6"/><i><font color="Green" title="E7">A1</font></i>: 
 <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c3">W</font> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V</font>
 ;<br/>

<b>hence </b><a NAME="E2:6"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W</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="c2">V</font>
 <b>by </b><i><a class="ref" href="vectsp_4.html#D2" title="VECTSP_4:def.2">VECTSP_4:def 2</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_4.html#D2" title="VECTSP_4:def.2">VECTSP_4:def 2</a><br/>

<b>thus </b> <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">W</font> = 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c3">W</font></span>)</span>

<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font>
<b>by </b><i><a class="txt" href="pencil_4.html#E1:6"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="vectsp_4.html#D2" title="VECTSP_4:def.2">VECTSP_4:def 2</a></i>
;<br/>

<b>thus </b><a NAME="E4:6"/>
( the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c3">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c2">V</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W</font> &amp; the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">lmult</a> of <font color="Maroon" title="c3">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="relat_1.html#K7" title="RELAT_1:func.7">K11</a>(the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">lmult</a> of <font color="Maroon" title="c2">V</font>,<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>) )
 <b>by </b><i><a class="txt" href="pencil_4.html#E1:6"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="vectsp_4.html#D2" title="VECTSP_4:def.2">VECTSP_4:def 2</a></i>;<br/>


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