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<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">Field</a>;<br/><b>let </b><font color="Maroon" title="c2">W1</font>, <font color="Maroon" title="c3">W2</font> be  <a href="matrlin.html#V2" title="MATRLIN:attr.2">finite-dimensional</a> <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">VectSp</a> of <font color="Maroon" title="c1">F</font>;<br/>



<b>assume </b><a NAME="E1:28"/><i><font color="Green" title="E28">A1</font></i>: 
 <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c2">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c3">W2</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<a NAME="E2:28"/>
 <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c2">W1</font> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of  <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c3">W2</font>
 
<b>by </b><i><a class="txt" href="pencil_4.html#E1:28"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="vectsp_4.html#T32" title="VECTSP_4:th.32">VECTSP_4:32</a></i>;<br/>
<a NAME="E3:28"/><b>then </b>
<font color="Maroon" title="c2">W1</font> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of  <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c3">W2</font>
 
<b>by </b><i><a class="ref" href="pencil_4.html#T6" target="_self" title="PENCIL_4:th.6">Th6</a></i>;<br/>
<a NAME="E4:28"/><b>then </b>
<font color="Maroon" title="c2">W1</font> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c3">W2</font>
 
<b>by </b><i><a class="ref" href="pencil_4.html#T4" target="_self" title="PENCIL_4:th.4">Th4</a></i>;<br/>
<b>hence </b><a NAME="E5:28"/>
<font color="Maroon" title="c4">m</font> <a href="vectsp_9.html#K2" title="VECTSP_9:func.2">Subspaces_of</a> <font color="Maroon" title="c2">W1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">m</font> <a href="vectsp_9.html#K2" title="VECTSP_9:func.2">Subspaces_of</a> <font color="Maroon" title="c3">W2</font>
 <b>by </b><i><a class="ref" href="vectsp_9.html#T42" title="VECTSP_9:th.42">VECTSP_9:42</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><br/>

<a NAME="E6:28"/>
 <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c3">W2</font> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of  <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c2">W1</font>
 
<b>by </b><i><a class="txt" href="pencil_4.html#E1:28"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="vectsp_4.html#T32" title="VECTSP_4:th.32">VECTSP_4:32</a></i>;<br/>
<a NAME="E7:28"/><b>then </b>
<font color="Maroon" title="c3">W2</font> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of  <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c2">W1</font>
 
<b>by </b><i><a class="ref" href="pencil_4.html#T6" target="_self" title="PENCIL_4:th.6">Th6</a></i>;<br/>
<a NAME="E8:28"/><b>then </b>
<font color="Maroon" title="c3">W2</font> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">W1</font>
 
<b>by </b><i><a class="ref" href="pencil_4.html#T4" target="_self" title="PENCIL_4:th.4">Th4</a></i>;<br/>
<b>hence </b><a NAME="E9:28"/>
<font color="Maroon" title="c4">m</font> <a href="vectsp_9.html#K2" title="VECTSP_9:func.2">Subspaces_of</a> <font color="Maroon" title="c3">W2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">m</font> <a href="vectsp_9.html#K2" title="VECTSP_9:func.2">Subspaces_of</a> <font color="Maroon" title="c2">W1</font>
 <b>by </b><i><a class="ref" href="vectsp_9.html#T42" title="VECTSP_9:th.42">VECTSP_9:42</a></i>;<br/>


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