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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="vectsp_5.html#M1" target="_self">Linear_Compl</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>







<a NAME="E1:57"/>
<font color="Maroon">c<sub>2</sub></font> <a href="vectsp_5.html#R1" target="_self">is_the_direct_sum_of</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="vectsp_5.html#T48" target="_self">Th48</a></i>;<br/>
<b>hence </b><a NAME="E2:57"/>
<font color="Maroon">c<sub>3</sub></font> <a href="vectsp_5.html#K1" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#G4">VectSpStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="vectsp_1.html#U2">lmult</a> of <font color="Maroon">c<sub>2</sub></font> #)
 <b>by </b><i><a class="ref" href="vectsp_5.html#D4" target="_self">Def4</a></i>;<br/>

<b>hence </b><a NAME="E3:57"/>
<font color="Maroon">c<sub>4</sub></font> <a href="vectsp_5.html#K1" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#G4">VectSpStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="vectsp_1.html#U2">lmult</a> of <font color="Maroon">c<sub>2</sub></font> #)
 <b>by </b><i><a class="txt" href="vectsp_5.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/>


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