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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">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">v</font>, <font color="Olive" title="b5">u1</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> holds <br/>( <font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Olive" title="b5">u1</font>,<font color="Olive" title="b6">v1</font> iff  ex <font color="Olive" title="b7">u2</font>, <font color="Olive" title="b8">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b7">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b8">v2</font> &amp; <font color="Olive" title="b7">u2</font>,<font color="Olive" title="b8">v2</font>,<font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b7">u2</font>,<font color="Olive" title="b8">v2</font>,<font color="Olive" title="b5">u1</font>,<font color="Olive" title="b6">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> ) )</span><br/><b>let </b><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">v</font>, <font color="Maroon" title="c6">u1</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:()"><i><font color="Red">::  thesis: </font></i></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> implies ( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> iff  ex <font color="Olive" title="b1">u2</font>, <font color="Olive" title="b2">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> ) ) )</span><br/>













<b>assume </b><a NAME="E1:39"/><i><font color="Green" title="E30">A1</font></i>: 
 <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> iff  ex <font color="Olive" title="b1">u2</font>, <font color="Olive" title="b2">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> ) )</span><br/>

<a NAME="E2:39"/>
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> iff  ex <font color="Olive" title="b1">u2</font>, <font color="Olive" title="b2">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>proof </b></a><div class="add">

<a NAME="E1:39_1"/><i><font color="Green" title="E31">A2</font></i>: 
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> implies  ex <font color="Olive" title="b1">u2</font>, <font color="Olive" title="b2">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:39_1_1"/><i><font color="Green" title="E32">A3</font></i>: 
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">u2</font>, <font color="Olive" title="b2">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )</span><br/>

<div><i><font color="Green" title="E33">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:39_1_1_1"/><i><font color="Green" title="E34">A5</font></i>: 
( <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> &amp; <font color="Maroon" title="c6">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">u2</font> being  <a href="subset_1.html#M1" title="SUBSET_1:mode.1">M2</a>(the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>) ex <font color="Olive" title="b2">v2</font>, <font color="Olive" title="b3">u2</font>, <font color="Olive" title="b4">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b3">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">v2</font> &amp; <font color="Olive" title="b3">u2</font>,<font color="Olive" title="b4">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b3">u2</font>,<font color="Olive" title="b4">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )</span><br/><b>take </b><font color="Maroon" title="c8">u2</font> =  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <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">  ex <font color="Olive" title="b1">v2</font>, <font color="Olive" title="b2">u2</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> st <br/>( <font color="Olive" title="b2">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">v2</font> &amp; <font color="Olive" title="b2">u2</font>,<font color="Olive" title="b3">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b2">u2</font>,<font color="Olive" title="b3">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )</span><br/><b>take </b><font color="Maroon" title="c9">v2</font> = <font color="Maroon" title="c2">x</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">u2</font>, <font color="Olive" title="b2">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )</span><br/><a NAME="E2:39_1_1_1"/>
(  <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">u2</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c9">v2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> &amp;  <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">u2</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c9">v2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> )
 <b>by </b><i><a class="txt" href="#E1:39_1_1_1"><i><font color="Green" title="E34">A5</font></i></a>, <a class="ref" href="analoaf.html#T18" title="ANALOAF:th.18">ANALOAF:18</a></i>;<br/><a NAME="E3:39_1_1_1"/><b>then </b><i><font color="Green" title="E35">A6</font></i>: 
( <font color="Maroon" title="c8">u2</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c8">u2</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )
 <b>by </b><i><a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></i>;<br/><a NAME="E4:39_1_1_1"/>
<font color="Maroon" title="c8">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">v2</font>
 <b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="analort.html#E4"><i><font color="Green" title="E4">Lm4</font></i></a></i>;<br/><b>hence </b><a NAME="E5:39_1_1_1"/>
 ex <font color="Olive" title="b1">u2</font>, <font color="Olive" title="b2">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )
 <b>by </b><i><a class="txt" href="#E3:39_1_1_1"><i><font color="Green" title="E35">A6</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>
<div><i><font color="Green" title="E34">A7</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:39_1_1_2"/><i><font color="Green" title="E35">A8</font></i>: 
<font color="Maroon" title="c4">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">v</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">u2</font>, <font color="Olive" title="b2">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )</span><br/><b>consider </b><font color="Maroon" title="c8">u2</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="E3:39_1_1_2"/><i><font color="Green" title="E36">A9</font></i>: 
 <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">u</font>
 <b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="analort.html#T8" target="_self" title="ANALORT:th.8">Th8</a></i>;<br/><b>consider </b><font color="Maroon" title="c9">v2</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="E5:39_1_1_2"/><i><font color="Green" title="E37">A10</font></i>: 
 <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c9">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font>
 <b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="analort.html#T8" target="_self" title="ANALORT:th.8">Th8</a></i>;<br/><a NAME="E6:39_1_1_2"/>
 <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">u2</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c9">v2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>
 <b>by </b><i><a class="txt" href="#E3:39_1_1_2"><i><font color="Green" title="E36">A9</font></i></a>, <a class="txt" href="#E5:39_1_1_2"><i><font color="Green" title="E37">A10</font></i></a>, <a class="ref" href="analoaf.html#T17" title="ANALOAF:th.17">ANALOAF:17</a></i>;<br/><a NAME="E7:39_1_1_2"/><b>then </b><i><font color="Green" title="E38">A11</font></i>: 
<font color="Maroon" title="c8">u2</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></i>;<br/><a NAME="E8:39_1_1_2"/>
<font color="Maroon" title="c8">u2</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="txt" href="#E1:39_1_1"><i><font color="Green" title="E32">A3</font></i></a>, <a class="txt" href="#E3:39_1_1_2"><i><font color="Green" title="E36">A9</font></i></a>, <a class="txt" href="#E5:39_1_1_2"><i><font color="Green" title="E37">A10</font></i></a>, <a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E9:39_1_1_2"/>
 ex <font color="Olive" title="b1">u2</font>, <font color="Olive" title="b2">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )
 <b>by </b><i><a class="txt" href="#E1:39_1_1_2"><i><font color="Green" title="E35">A8</font></i></a>, <a class="txt" href="#E3:39_1_1_2"><i><font color="Green" title="E36">A9</font></i></a>, <a class="txt" href="#E5:39_1_1_2"><i><font color="Green" title="E37">A10</font></i></a>, <a class="txt" href="#E7:39_1_1_2"><i><font color="Green" title="E38">A11</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>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:39_1_1_3"/><i><font color="Green" title="E35">A12</font></i>: 
<font color="Maroon" title="c6">u1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">v1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">u2</font>, <font color="Olive" title="b2">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )</span><br/><b>consider </b><font color="Maroon" title="c8">u2</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="E3:39_1_1_3"/><i><font color="Green" title="E36">A13</font></i>: 
 <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u1</font>
 <b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="analort.html#T8" target="_self" title="ANALORT:th.8">Th8</a></i>;<br/><b>consider </b><font color="Maroon" title="c9">v2</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="E5:39_1_1_3"/><i><font color="Green" title="E37">A14</font></i>: 
 <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c9">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v1</font>
 <b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="analort.html#T8" target="_self" title="ANALORT:th.8">Th8</a></i>;<br/><a NAME="E6:39_1_1_3"/>
 <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">u2</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c9">v2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font>
 <b>by </b><i><a class="txt" href="#E3:39_1_1_3"><i><font color="Green" title="E36">A13</font></i></a>, <a class="txt" href="#E5:39_1_1_3"><i><font color="Green" title="E37">A14</font></i></a>, <a class="ref" href="analoaf.html#T17" title="ANALOAF:th.17">ANALOAF:17</a></i>;<br/><a NAME="E7:39_1_1_3"/><b>then </b><i><font color="Green" title="E38">A15</font></i>: 
<font color="Maroon" title="c8">u2</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></i>;<br/><a NAME="E8:39_1_1_3"/>
 <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">u2</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c9">v2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>
 <b>by </b><i><a class="txt" href="#E1:39_1_1"><i><font color="Green" title="E32">A3</font></i></a>, <a class="txt" href="#E3:39_1_1_3"><i><font color="Green" title="E36">A13</font></i></a>, <a class="txt" href="#E5:39_1_1_3"><i><font color="Green" title="E37">A14</font></i></a>, <a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</a></i>;<br/><a NAME="E9:39_1_1_3"/><b>then </b>
<font color="Maroon" title="c8">u2</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E10:39_1_1_3"/>
 ex <font color="Olive" title="b1">u2</font>, <font color="Olive" title="b2">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )
 <b>by </b><i><a class="txt" href="#E1:39_1_1_3"><i><font color="Green" title="E35">A12</font></i></a>, <a class="txt" href="#E3:39_1_1_3"><i><font color="Green" title="E36">A13</font></i></a>, <a class="txt" href="#E5:39_1_1_3"><i><font color="Green" title="E37">A14</font></i></a>, <a class="txt" href="#E7:39_1_1_3"><i><font color="Green" title="E38">A15</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>hence </b><a NAME="E5:39_1_1"/>
 ex <font color="Olive" title="b1">u2</font>, <font color="Olive" title="b2">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )
 <b>by </b><i><a class="txt" href="#E2:39_1_1"><i><font color="Green" title="E33">A4</font></i></a>, <a class="txt" href="#E3:39_1_1"><i><font color="Green" title="E34">A7</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>
<a NAME="E2:39_1"/>
(  ex <font color="Olive" title="b1">u2</font>, <font color="Olive" title="b2">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> ) implies <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_2"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon" title="c8">u2</font>, <font color="Maroon" title="c9">v2</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><a NAME="E2:39_1_2"/><i><font color="Green" title="E32">A16</font></i>: 
( <font color="Maroon" title="c8">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">v2</font> &amp; <font color="Maroon" title="c8">u2</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c8">u2</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font></span><br/>

<a NAME="E3:39_1_2"/>
(  <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">u2</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c9">v2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> &amp;  <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">u2</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c9">v2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> )
 
<b>by </b><i><a class="txt" href="#E2:39_1_2"><i><font color="Green" title="E32">A16</font></i></a>, <a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E4:39_1_2"/>
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font>
 <b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="#E2:39_1_2"><i><font color="Green" title="E32">A16</font></i></a>, <a class="ref" href="analort.html#T6" target="_self" title="ANALORT:th.6">Th6</a>, <a class="ref" href="analoaf.html#T20" title="ANALOAF:th.20">ANALOAF:20</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>hence </b><a NAME="E3:39_1"/>
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> iff  ex <font color="Olive" title="b1">u2</font>, <font color="Olive" title="b2">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> ) )
 <b>by </b><i><a class="txt" href="#E1:39_1"><i><font color="Green" title="E31">A2</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>hence </b><a NAME="E3:39"/>
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> iff  ex <font color="Olive" title="b1">u2</font>, <font color="Olive" title="b2">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">u2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
