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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">vector-distributive</a>   <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">scalar-distributive</a>   <a href="rlvect_1.html#V7" title="RLVECT_1:attr.7">scalar-associative</a>   <a href="rlvect_1.html#V8" title="RLVECT_1:attr.8">scalar-unital</a>   <a href="rlvect_1.html#L1" title="RLVECT_1:struct.1">RLSStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">LR</font> being    <a href="rlvect_2.html#M1" title="RLVECT_2:mode.1">Linear_Combination</a> of <font color="Maroon" title="c1">R</font> holds  1 <a href="rlaffin1.html#K2" title="RLAFFIN1:func.2">(*)</a> <font color="Olive" title="b1">LR</font> <a href="rlvect_2.html#R1" title="RLVECT_2:pred.1">=</a> <font color="Olive" title="b1">LR</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">LR</font> be    <a href="rlvect_2.html#M1" title="RLVECT_2:mode.1">Linear_Combination</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> 1 <a href="rlaffin1.html#K2" title="RLAFFIN1:func.2">(*)</a> <font color="Maroon" title="c2">LR</font> <a href="rlvect_2.html#R1" title="RLVECT_2:pred.1">=</a> <font color="Maroon" title="c2">LR</font></span><br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">v</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default">1 <a href="rlaffin1.html#K2" title="RLAFFIN1:func.2">(*)</a> <font color="Maroon" title="c2">LR</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">LR</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">v</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default">1 <a href="rlaffin1.html#K2" title="RLAFFIN1:func.2">(*)</a> <font color="Maroon" title="c2">LR</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">v</font> = 
<font color="Maroon" title="c2">LR</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K2" title="REAL_1:func.2">"</a></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">v</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlaffin1.html#D2" target="_self" title="RLAFFIN1:def.2">Def2</a></span>
<br/>.= 
<font color="Maroon" title="c2">LR</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">v</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D8" title="RLVECT_1:def.8">RLVECT_1:def 8</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:35"/>
1 <a href="rlaffin1.html#K2" title="RLAFFIN1:func.2">(*)</a> <font color="Maroon" title="c2">LR</font> <a href="rlvect_2.html#R1" title="RLVECT_2:pred.1">=</a> <font color="Maroon" title="c2">LR</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_2.html#D9" title="RLVECT_2:def.9">RLVECT_2:def 9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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