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<span class="kw">let </span><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#G1" title="RLVECT_1:aggr.1">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>  #); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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></span><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="valued_1.html#K3" title="VALUED_1:func.3">+</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rsspace.html#D4" target="_self" title="RSSPACE:def.4">Def4</a></span>
<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="valued_1.html#K3" title="VALUED_1:func.3">+</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="valued_1.html#K3" title="VALUED_1:func.3">+</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rsspace.html#D4" target="_self" title="RSSPACE:def.4">Def4</a></span>
<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="valued_1.html#K3" title="VALUED_1:func.3">+</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="valued_1.html#K3" title="VALUED_1:func.3">+</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rsspace.html#T3" target="_self" title="RSSPACE:th.3">Th3</a></span>
<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="valued_1.html#K3" title="VALUED_1:func.3">+</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="valued_1.html#K3" title="VALUED_1:func.3">+</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="seq_1.html#T20" title="SEQ_1:th.20">SEQ_1:20</a></span>
<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="valued_1.html#K3" title="VALUED_1:func.3">+</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="valued_1.html#K3" title="VALUED_1:func.3">+</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rsspace.html#T3" target="_self" title="RSSPACE:th.3">Th3</a></span>
<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="valued_1.html#K3" title="VALUED_1:func.3">+</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rsspace.html#D4" target="_self" title="RSSPACE:def.4">Def4</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:12"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rsspace.html#D4" target="_self" title="RSSPACE:def.4">Def4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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