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<b>let </b><font color="Maroon" title="c1">u</font>, <font color="Maroon" title="c2">v</font>, <font color="Maroon" title="c3">w</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <a href="rsspace.html#K1" title="RSSPACE:func.1">the_set_of_RealSequences</a> ,<a href="rsspace.html#K6" title="RSSPACE:func.6">Zeroseq</a> ,<a href="rsspace.html#K4" title="RSSPACE:func.4">l_add</a> ,<a href="rsspace.html#K5" title="RSSPACE:func.5">l_mult</a>  #);<br/>

<span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">w</font> = 
<span class="p1">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c2">v</font></span>)</span></span>)</span> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p1">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <font color="Maroon" title="c3">w</font></span>)</span>
<b>by </b><i><a class="ref" href="rsspace.html#T4" target="_self" title="RSSPACE:th.4">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <font color="Maroon" title="c1">u</font></span>)</span> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p3">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <font color="Maroon" title="c2">v</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p1">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <font color="Maroon" title="c3">w</font></span>)</span>
<b>by </b><i><a class="ref" href="rsspace.html#T4" target="_self" title="RSSPACE:th.4">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <font color="Maroon" title="c1">u</font></span>)</span> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p2">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <font color="Maroon" title="c2">v</font></span>)</span></span>)</span> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p1">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <font color="Maroon" title="c3">w</font></span>)</span>
<b>by </b><i><a class="ref" href="rsspace.html#T3" target="_self" title="RSSPACE:th.3">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <font color="Maroon" title="c1">u</font></span>)</span> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p2">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T20" title="SEQ_1:th.20">SEQ_1:20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <font color="Maroon" title="c1">u</font></span>)</span> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p1">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p3">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rsspace.html#T3" target="_self" title="RSSPACE:th.3">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <font color="Maroon" title="c1">u</font></span>)</span> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p1">(<span class="default"><a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rsspace.html#T4" target="_self" title="RSSPACE:th.4">Th4</a></i>
;<br/>
<b>hence </b><a NAME="E2:13"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">w</font></span>)</span>
 <b>by </b><i><a class="ref" href="rsspace.html#T4" target="_self" title="RSSPACE:th.4">Th4</a></i>;<br/>


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