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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><br/> for <font color="Olive" title="b4">W</font> being   <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c1">V</font>  st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">v1</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Olive" title="b4">W</font> &amp; <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">v2</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Olive" title="b4">W</font> holds <br/><font color="Olive" title="b2">v1</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Olive" title="b4">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v2</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Olive" title="b4">W</font></span><br/><b>let </b><font color="Maroon" title="c2">u</font>, <font color="Maroon" title="c3">v1</font>, <font color="Maroon" title="c4">v2</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">W</font> being   <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c1">V</font>  st <font color="Maroon" title="c2">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v1</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Olive" title="b1">W</font> &amp; <font color="Maroon" title="c2">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v2</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Olive" title="b1">W</font> holds <br/><font color="Maroon" title="c3">v1</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Olive" title="b1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v2</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Olive" title="b1">W</font></span><br/><b>let </b><font color="Maroon" title="c5">W</font> be    <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v1</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font> &amp; <font color="Maroon" title="c2">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v2</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font> implies <font color="Maroon" title="c3">v1</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v2</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font> )</span><br/>









<b>assume </b><b>that </b><br/><a NAME="E1:59"/><i><font color="Green" title="E44">A1</font></i>: 
<font color="Maroon" title="c2">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v1</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font>
 <b>and </b><br/><a NAME="E2:59"/><i><font color="Green" title="E45">A2</font></i>: 
<font color="Maroon" title="c2">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v2</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">v1</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v2</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font></span><br/>

<b>consider </b><font color="Maroon" title="c6">x1</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E4:59"/><i><font color="Green" title="E46">A3</font></i>: 
<font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">x1</font>
 <b>and </b><br/><a NAME="E5:59"/><i><font color="Green" title="E47">A4</font></i>: 
<font color="Maroon" title="c6">x1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c5">W</font>
 <b>by </b><i><a class="txt" href="rlsub_1.html#E1:59"><i><font color="Green" title="E44">A1</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">x2</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E7:59"/><i><font color="Green" title="E48">A5</font></i>: 
<font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v2</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">x2</font>
 <b>and </b><br/><a NAME="E8:59"/><i><font color="Green" title="E49">A6</font></i>: 
<font color="Maroon" title="c7">x2</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c5">W</font>
 <b>by </b><i><a class="txt" href="rlsub_1.html#E2:59"><i><font color="Green" title="E45">A2</font></i></a></i>;<br/>
<b>thus </b><a NAME="E9:59"/>
<font color="Maroon" title="c3">v1</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">v2</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">v2</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">v1</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v1</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v2</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font> )</span><br/>

<b>assume </b><a NAME="E1:59_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v1</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v2</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font></span><br/>

<b>then consider </b><font color="Maroon" title="c9">u1</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E3:59_1"/><i><font color="Green" title="E50">A7</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">u1</font>
 <b>and </b><br/><a NAME="E4:59_1"/><i><font color="Green" title="E51">A8</font></i>: 
<font color="Maroon" title="c9">u1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c5">W</font>
 ;<br/>
<font color="Maroon" title="c2">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">x1</font> = 
<font color="Maroon" title="c3">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">x1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">x1</font></span>)</span>
<b>by </b><i><a class="txt" href="rlsub_1.html#E4:59"><i><font color="Green" title="E46">A3</font></i></a>, <a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c3">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T28" title="RLVECT_1:th.28">RLVECT_1:28</a></i>
<br/>.= 
<font color="Maroon" title="c3">v1</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10" title="RLVECT_1:th.10">RLVECT_1:10</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E52">A9</font></i>: <font color="Maroon" title="c8">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">x1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">u1</font>
<b>by </b><i><a class="txt" href="rlsub_1.html#E7:59"><i><font color="Green" title="E48">A5</font></i></a>, <a class="txt" href="rlsub_1.html#E3:59_1"><i><font color="Green" title="E50">A7</font></i></a>, <a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c4">v2</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">x1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">u1</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>
;<br/>
<a NAME="E7:59_1"/>
<font color="Maroon" title="c7">x2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">x1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c5">W</font>
 
<b>by </b><i><a class="txt" href="rlsub_1.html#E5:59"><i><font color="Green" title="E47">A4</font></i></a>, <a class="txt" href="rlsub_1.html#E8:59"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="rlsub_1.html#T31" target="_self" title="RLSUB_1:th.31">Th31</a></i>;<br/>
<a NAME="E8:59_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">x1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">u1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c5">W</font>
 
<b>by </b><i><a class="txt" href="rlsub_1.html#E4:59_1"><i><font color="Green" title="E51">A8</font></i></a>, <a class="ref" href="rlsub_1.html#T28" target="_self" title="RLSUB_1:th.28">Th28</a></i>;<br/>
<b>hence </b><a NAME="E9:59_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v2</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font>
 <b>by </b><i><a class="txt" href="rlsub_1.html#E6:59_1"><i><font color="Green" title="E52">A9</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v2</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v1</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font> )</span><br/>

<b>assume </b><a NAME="E10:59"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v2</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v1</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font></span><br/>

<b>then consider </b><font color="Maroon" title="c9">u1</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E12:59"/><i><font color="Green" title="E50">A10</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v2</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">u1</font>
 <b>and </b><br/><a NAME="E13:59"/><i><font color="Green" title="E51">A11</font></i>: 
<font color="Maroon" title="c9">u1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c5">W</font>
 ;<br/>
<font color="Maroon" title="c2">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c7">x2</font> = 
<font color="Maroon" title="c4">v2</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c7">x2</font></span>)</span>
<b>by </b><i><a class="txt" href="rlsub_1.html#E7:59"><i><font color="Green" title="E48">A5</font></i></a>, <a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c4">v2</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T28" title="RLVECT_1:th.28">RLVECT_1:28</a></i>
<br/>.= 
<font color="Maroon" title="c4">v2</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10" title="RLVECT_1:th.10">RLVECT_1:10</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E52">A12</font></i>: <font color="Maroon" title="c8">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">x1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c7">x2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">u1</font>
<b>by </b><i><a class="txt" href="rlsub_1.html#E4:59"><i><font color="Green" title="E46">A3</font></i></a>, <a class="txt" href="rlsub_1.html#E12:59"><i><font color="Green" title="E50">A10</font></i></a>, <a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c3">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">x1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c7">x2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">u1</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>
;<br/>
<a NAME="E16:59"/>
<font color="Maroon" title="c6">x1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c7">x2</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c5">W</font>
 
<b>by </b><i><a class="txt" href="rlsub_1.html#E5:59"><i><font color="Green" title="E47">A4</font></i></a>, <a class="txt" href="rlsub_1.html#E8:59"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="rlsub_1.html#T31" target="_self" title="RLSUB_1:th.31">Th31</a></i>;<br/>
<a NAME="E17:59"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">x1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c7">x2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">u1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c5">W</font>
 
<b>by </b><i><a class="txt" href="rlsub_1.html#E13:59"><i><font color="Green" title="E51">A11</font></i></a>, <a class="ref" href="rlsub_1.html#T28" target="_self" title="RLSUB_1:th.28">Th28</a></i>;<br/>
<b>hence </b><a NAME="E18:59"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v1</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c5">W</font>
 <b>by </b><i><a class="txt" href="rlsub_1.html#E15:59"><i><font color="Green" title="E52">A12</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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