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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">L</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   <a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <font color="Olive" title="b1">L</font></span>)</span> <a href="rlvect_2.html#R1" title="RLVECT_2:pred.1">=</a> <font color="Olive" title="b1">L</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">L</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">  <a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <font color="Maroon" title="c2">L</font></span>)</span> <a href="rlvect_2.html#R1" title="RLVECT_2:pred.1">=</a> <font color="Maroon" title="c2">L</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">v</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="rlvect_2.html#D11" target="_self" title="RLVECT_2:def.11">RLVECT_2:def 11</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"><a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <font color="Maroon" title="c2">L</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">L</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">v</font></span><br/>





<span class="kw">thus </span><span class="p1">(<span class="default"><a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <font color="Maroon" title="c2">L</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">v</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span>)</span> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c2">L</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">v</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_2.html#T70" target="_self" title="RLVECT_2:th.70">Th70</a></span>
<br/>.= 
1 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">L</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">v</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_2.html#D13" target="_self" title="RLVECT_2:def.13">Def13</a></span>
<br/>.= 
<font color="Maroon" title="c2">L</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">v</font>

; <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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