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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">W1</font>, <font color="Maroon" title="c3">W2</font> be    <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c1">V</font>;<br/>





<b>assume </b><a NAME="E1:43"/>
<font color="Maroon" title="c1">V</font> <a href="rlsub_2.html#R1" title="RLSUB_2:pred.1">is_the_direct_sum_of</a> <font color="Maroon" title="c2">W1</font>,<font color="Maroon" title="c3">W2</font>
 ;<br/>

<a NAME="E2:43"/><b>then </b>
(  <a href="rlvect_1.html#G1" title="RLVECT_1:aggr.1">RLSStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">U2</a> of <font color="Maroon" title="c1">V</font>,the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">V</font>,the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c1">V</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <font color="Maroon" title="c3">W2</font> &amp; <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlsub_1.html#K1" title="RLSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font> )
 
<b>by </b><i><a class="ref" href="rlsub_2.html#D4" target="_self" title="RLSUB_2:def.4">Def4</a></i>;<br/>
<a NAME="E3:43"/><b>then </b>
(  <a href="rlvect_1.html#G1" title="RLVECT_1:aggr.1">RLSStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">U2</a> of <font color="Maroon" title="c1">V</font>,the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">V</font>,the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c1">V</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W2</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <font color="Maroon" title="c2">W1</font> &amp; <font color="Maroon" title="c3">W2</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c2">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlsub_1.html#K1" title="RLSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font> )
 
<b>by </b><i><a class="txt" href="rlsub_2.html#E10"><i><font color="Green" title="E6">Lm1</font></i></a>, <a class="ref" href="rlsub_2.html#T18" target="_self" title="RLSUB_2:th.18">Th18</a></i>;<br/>
<b>hence </b><a NAME="E4:43"/>
<font color="Maroon" title="c1">V</font> <a href="rlsub_2.html#R1" title="RLSUB_2:pred.1">is_the_direct_sum_of</a> <font color="Maroon" title="c3">W2</font>,<font color="Maroon" title="c2">W1</font>
 <b>by </b><i><a class="ref" href="rlsub_2.html#D4" target="_self" title="RLSUB_2:def.4">Def4</a></i>;<br/>


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