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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">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">u1</font>, <font color="Olive" title="b5">v</font>, <font color="Olive" title="b6">v1</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  st  <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">u1</font>,<font color="Olive" title="b5">v</font>,<font color="Olive" title="b6">v1</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> holds <br/><font color="Olive" title="b5">v</font>,<font color="Olive" title="b6">v1</font>,<font color="Olive" title="b4">u1</font>,<font color="Olive" title="b3">u</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">u</font>, <font color="Maroon" title="c5">u1</font>, <font color="Maroon" title="c6">v</font>, <font color="Maroon" title="c7">v1</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> implies <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">u</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )</span><br/>













<span class="kw">assume </span><a NAME="E1:29"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
 <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> or <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">u</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:29"/>
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 ; <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="c6">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">u</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span><br/>

<a NAME="E3:29"/><span class="kw">then </span>
 <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">u1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analort.html#D3" target="_self" title="ANALORT:def.3">Def3</a></span>;<br/>
<a NAME="E4:29"/><span class="kw">then </span>
<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a>  <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">u1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</a></span>;<br/>
<a NAME="E5:29"/><span class="kw">then </span>
 <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c6">v</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c7">v1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a>  <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font></span>)</span>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">u1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="analort.html#T16" target="_self" title="ANALORT:th.16">Th16</a></span>;<br/>
<a NAME="E6:29"/><span class="kw">then </span>
 <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c6">v</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c7">v1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">u</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">u1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="analort.html#T14" target="_self" title="ANALORT:th.14">Th14</a></span>;<br/>
<a NAME="E7:29"/><span class="kw">then </span>
 <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c6">v</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c7">v1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">u</font>, <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">u1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="analort.html#T14" target="_self" title="ANALORT:th.14">Th14</a></span>;<br/>
<a NAME="E8:29"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A2</font></span>: 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">u</font>, <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">u1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a>  <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c6">v</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c7">v1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</a></span>;<br/>
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">u1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span> = 
<font color="Maroon" title="c4">u</font> <a href="analort.html#K1" title="ANALORT:func.1">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">u1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T30" title="RLVECT_1:th.30">RLVECT_1:30</a></span>
<br/>.= 
<font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u1</font>

;<br/>
<a NAME="E10:29"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A3</font></span>: 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">u</font>, <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">u1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">u</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#T24" title="ANALOAF:th.24">ANALOAF:24</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E30">A4</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="29_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:29_2"/>
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">u1</font>
 ; <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="c6">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">u</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span><br/><a NAME="E2:29_2"/><span class="kw">then </span>
 <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c6">v</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c7">v1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">u</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:29"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="txt" href="#E10:29"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="analoaf.html#T20" title="ANALOAF:th.20">ANALOAF:20</a></span>;<br/><span class="kw">hence </span><a NAME="E3:29_2"/>
<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">u</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analort.html#D3" target="_self" title="ANALORT:def.3">Def3</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/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:29_3"/>
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">u1</font>
 ; <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="c6">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">u</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span><br/><span class="kw">then </span><font color="Maroon" title="c4">u</font> = 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">u1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T30" title="RLVECT_1:th.30">RLVECT_1:30</a></span>
<br/>.= 
<font color="Maroon" title="c5">u1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T30" title="RLVECT_1:th.30">RLVECT_1:30</a></span>
;<br/><a NAME="E3:29_3"/><span class="kw">then </span>
 <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c6">v</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c7">v1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">u</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#T18" title="ANALOAF:th.18">ANALOAF:18</a></span>;<br/><span class="kw">hence </span><a NAME="E4:29_3"/>
<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">u</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analort.html#D3" target="_self" title="ANALORT:def.3">Def3</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E13:29"/>
<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">u</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:29"><span class="lab"><font color="Green" title="E30">A4</font></span></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/>


</div>
