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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">L1</font>, <font color="Olive" title="b2">L2</font> being   <a href="rlvect_2.html#M1" title="RLVECT_2:mode.1">Linear_Combination</a> of <font color="Maroon" title="c1">V</font> holds  <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K16" title="RLVECT_2:func.16">LC_RLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Olive" title="b1">L1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K16" title="RLVECT_2:func.16">LC_RLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Olive" title="b2">L2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">L1</font> <a href="rlvect_2.html#K10" title="RLVECT_2:func.10">-</a> <font color="Olive" title="b2">L2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">L1</font>, <font color="Maroon" title="c3">L2</font> be    <a href="rlvect_2.html#M1" title="RLVECT_2:mode.1">Linear_Combination</a> of <font color="Maroon" title="c1">V</font>; <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"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K16" title="RLVECT_2:func.16">LC_RLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">L1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K16" title="RLVECT_2:func.16">LC_RLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c3">L2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">L1</font> <a href="rlvect_2.html#K10" title="RLVECT_2:func.10">-</a> <font color="Maroon" title="c3">L2</font></span><br/>





<a NAME="E1:112"/>
 <a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <font color="Maroon" title="c3">L2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_2.html#D16" target="_self" title="RLVECT_2:def.16">Def16</a></span>;<br/>
<a NAME="E2:112"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A1</font></span>: 
 <a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <font color="Maroon" title="c3">L2</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="rlvect_2.html#K16" title="RLVECT_2:func.16">LC_RLSpace</a> <font color="Maroon" title="c1">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></span>;<br/>
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K16" title="RLVECT_2:func.16">LC_RLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c3">L2</font></span>)</span> = 
 <a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <font color="Maroon" title="c3">L2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_2.html#T98" target="_self" title="RLVECT_2:th.98">Th98</a></span>
<br/>.= 
 <a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K16" title="RLVECT_2:func.16">LC_RLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <font color="Maroon" title="c3">L2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:112"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="rlvect_2.html#D1" target="_self" title="RLVECT_2:def.1">Def1</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:112"/>
<span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K16" title="RLVECT_2:func.16">LC_RLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">L1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K16" title="RLVECT_2:func.16">LC_RLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c3">L2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">L1</font> <a href="rlvect_2.html#K10" title="RLVECT_2:func.10">-</a> <font color="Maroon" title="c3">L2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_2.html#T96" target="_self" title="RLVECT_2:th.96">Th96</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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