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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> be  <a href="matrlin.html#V2" title="MATRLIN:attr.2">finite-dimensional</a> <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">F</font>;<br/><b>let </b><font color="Maroon" title="c3">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c4">W1</font>, <font color="Maroon" title="c5">W2</font>, <font color="Maroon" title="c6">W</font> be    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V</font>;<br/>







<b>assume </b><a NAME="E1:11"/><i><font color="Green" title="E10">A1</font></i>: 
<font color="Maroon" title="c6">W</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pencil_4.html#K3" title="PENCIL_4:func.3">pencil</a> <font color="Maroon" title="c4">W1</font>,<font color="Maroon" title="c5">W2</font>,<font color="Maroon" title="c3">k</font>
 ;<br/>

<a NAME="E2:11"/><b>then </b><i><font color="Green" title="E11">A2</font></i>: 
( <font color="Maroon" title="c6">W</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pencil_4.html#K2" title="PENCIL_4:func.2">pencil</a> <font color="Maroon" title="c4">W1</font>,<font color="Maroon" title="c5">W2</font> &amp; <font color="Maroon" title="c6">W</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">k</font> <a href="vectsp_9.html#K2" title="VECTSP_9:func.2">Subspaces_of</a> <font color="Maroon" title="c2">V</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">X</font> being  <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>  <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V</font><b> such that </b><br/><a NAME="E4:11"/><i><font color="Green" title="E12">A3</font></i>: 
( <font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">X</font> &amp;  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c7">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> )
 <b>by </b><i><a class="txt" href="pencil_4.html#E1:11"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="vectsp_9.html#D3" title="VECTSP_9:def.3">VECTSP_9:def 3</a></i>;<br/>
<a NAME="E5:11"/><i><font color="Green" title="E13">A4</font></i>: 
<font color="Maroon" title="c6">W</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pencil_4.html#K1" title="PENCIL_4:func.1">segment</a> <font color="Maroon" title="c4">W1</font>,<font color="Maroon" title="c5">W2</font>
 
<b>by </b><i><a class="txt" href="pencil_4.html#E2:11"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E6:11"/><b>then </b>
<font color="Maroon" title="c4">W1</font> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c5">W2</font>
 
<b>by </b><i><a class="ref" href="pencil_4.html#D1" target="_self" title="PENCIL_4:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E7:11"/>
( <font color="Maroon" title="c4">W1</font> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c6">W</font> &amp; <font color="Maroon" title="c6">W</font> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c5">W2</font> )
 <b>by </b><i><a class="txt" href="pencil_4.html#E4:11"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="pencil_4.html#E5:11"><i><font color="Green" title="E13">A4</font></i></a>, <a class="ref" href="pencil_4.html#D1" target="_self" title="PENCIL_4:def.1">Def1</a></i>;<br/>


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