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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/>

<a NAME="E1:55"/>
( <span class="p1">(<span class="default"><a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rlsub_2.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><a href="rlsub_1.html#K2">(Omega).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#G2">RLSStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="rlvect_1.html#U2">Mult</a> of <font color="Maroon">c<sub>1</sub></font> #) &amp;  <a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rlsub_2.html#K2" target="_self">/\</a> <span class="p1">(<span class="default"><a href="rlsub_1.html#K2">(Omega).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="rlsub_2.html#T14" target="_self">Th14</a>, <a class="ref" href="rlsub_2.html#T22" target="_self">Th22</a></i>;<br/>
<b>hence </b><a NAME="E2:55"/>
<font color="Maroon">c<sub>1</sub></font> <a href="rlsub_2.html#R1" target="_self">is_the_direct_sum_of</a>  <a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font>, <a href="rlsub_1.html#K2">(Omega).</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="rlsub_2.html#D4" target="_self">Def4</a></i>;<br/>

<b>hence </b><a NAME="E3:55"/>
<font color="Maroon">c<sub>1</sub></font> <a href="rlsub_2.html#R1" target="_self">is_the_direct_sum_of</a>  <a href="rlsub_1.html#K2">(Omega).</a> <font color="Maroon">c<sub>1</sub></font>, <a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="rlsub_2.html#E60"><i><font color="Green">Lemma40</font></i></a></i>;<br/>


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