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<span class="kw">let </span><font color="Maroon" title="c4">L1</font>, <font color="Maroon" title="c5">L2</font> be    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Maroon" title="c2">A</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#K6" title="RLVECT_2:func.6">Sum</a> <font color="Maroon" title="c4">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> &amp;  <a href="rlaffin1.html#K3" title="RLAFFIN1:func.3">sum</a> <font color="Maroon" title="c4">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <a href="rlvect_2.html#K6" title="RLVECT_2:func.6">Sum</a> <font color="Maroon" title="c5">L2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> &amp;  <a href="rlaffin1.html#K3" title="RLAFFIN1:func.3">sum</a> <font color="Maroon" title="c5">L2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies <font color="Maroon" title="c4">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">L2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:94_1_2"/><span class="lab"><font color="Green" title="E70">A3</font></span>: 
 <a href="rlvect_2.html#K6" title="RLVECT_2:func.6">Sum</a> <font color="Maroon" title="c4">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font>
 <span class="kw">and </span><br/><a NAME="E2:94_1_2"/><span class="lab"><font color="Green" title="E71">A4</font></span>: 
 <a href="rlaffin1.html#K3" title="RLAFFIN1:func.3">sum</a> <font color="Maroon" title="c4">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">and </span><br/><a NAME="E3:94_1_2"/><span class="lab"><font color="Green" title="E72">A5</font></span>: 
 <a href="rlvect_2.html#K6" title="RLVECT_2:func.6">Sum</a> <font color="Maroon" title="c5">L2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font>
 <span class="kw">and </span><br/><a NAME="E4:94_1_2"/><span class="lab"><font color="Green" title="E73">A6</font></span>: 
 <a href="rlaffin1.html#K3" title="RLAFFIN1:func.3">sum</a> <font color="Maroon" title="c5">L2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">L2</font></span><br/>

<span class="lab"><font color="Green" title="E74">A7</font></span>:  <a href="rlvect_2.html#K6" title="RLVECT_2:func.6">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L1</font> <a href="rlvect_2.html#K10" title="RLVECT_2:func.10">-</a> <font color="Maroon" title="c5">L2</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="rlvect_2.html#K6" title="RLVECT_2:func.6">Sum</a> <font color="Maroon" title="c4">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#K6" title="RLVECT_2:func.6">Sum</a> <font color="Maroon" title="c4">L1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:94_1_2"><span class="lab"><font color="Green" title="E70">A3</font></span></a>, <a class="txt" href="#E3:94_1_2"><span class="lab"><font color="Green" title="E72">A5</font></span></a>, <a class="ref" href="rlvect_3.html#T4" title="RLVECT_3:th.4">RLVECT_3:4</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T28" title="RLVECT_1:th.28">RLVECT_1:28</a></span>
;<br/>
<a NAME="E6:94_1_2"/><span class="lab"><font color="Green" title="E75">A8</font></span>: 
<font color="Maroon" title="c4">L1</font> <a href="rlvect_2.html#K10" title="RLVECT_2:func.10">-</a> <font color="Maroon" title="c5">L2</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_2.html#T81" title="RLVECT_2:th.81">RLVECT_2:81</a></span>;<br/>
 <a href="rlaffin1.html#K3" title="RLAFFIN1:func.3">sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L1</font> <a href="rlvect_2.html#K10" title="RLVECT_2:func.10">-</a> <font color="Maroon" title="c5">L2</font></span>)</span> = 
1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:94_1_2"><span class="lab"><font color="Green" title="E71">A4</font></span></a>, <a class="txt" href="#E4:94_1_2"><span class="lab"><font color="Green" title="E73">A6</font></span></a>, <a class="ref" href="rlaffin1.html#T36" target="_self" title="RLAFFIN1:th.36">Th36</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 

;<br/>
<a NAME="E8:94_1_2"/><span class="kw">then </span>
 <a href="rlvect_2.html#K3" title="RLVECT_2:func.3">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L1</font> <a href="rlvect_2.html#K10" title="RLVECT_2:func.10">-</a> <font color="Maroon" title="c5">L2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:94"><span class="lab"><font color="Green" title="E68">A1</font></span></a>, <a class="txt" href="#E5:94_1_2"><span class="lab"><font color="Green" title="E74">A7</font></span></a>, <a class="txt" href="#E6:94_1_2"><span class="lab"><font color="Green" title="E75">A8</font></span></a>, <a class="ref" href="rlaffin1.html#T42" target="_self" title="RLAFFIN1:th.42">Th42</a></span>;<br/>
<a NAME="E9:94_1_2"/><span class="kw">then </span>
 <a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font> <a href="rlvect_2.html#R1" title="RLVECT_2:pred.1">=</a> <font color="Maroon" title="c4">L1</font> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <font color="Maroon" title="c5">L2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_2.html#D7" title="RLVECT_2:def.7">RLVECT_2:def 7</a></span>;<br/>
<a NAME="E10:94_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E76">A9</font></span>: 
 <a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <font color="Maroon" title="c5">L2</font> <a href="rlvect_2.html#R1" title="RLVECT_2:pred.1">=</a>  <a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <font color="Maroon" title="c4">L1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_2.html#T74" title="RLVECT_2:th.74">RLVECT_2:74</a></span>;<br/>
<a NAME="E11:94_1_2"/>
<font color="Maroon" title="c4">L1</font> <a href="rlvect_2.html#R1" title="RLVECT_2:pred.1">=</a>  <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="c4">L1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_2.html#T77" title="RLVECT_2:th.77">RLVECT_2:77</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:94_1_2"/>
<font color="Maroon" title="c4">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">L2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:94_1_2"><span class="lab"><font color="Green" title="E76">A9</font></span></a>, <a class="ref" href="rlvect_2.html#T77" title="RLVECT_2:th.77">RLVECT_2:77</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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