<?xml version="1.0"?>
<div class="add">

<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> 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/> ex <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">v</font>, <font color="Olive" title="b5">w</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">u</font>,<font color="Olive" title="b4">v</font>,<font color="Olive" title="b3">u</font>,<font color="Olive" title="b5">w</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; ( for <font color="Olive" title="b6">v1</font>, <font color="Olive" title="b7">w1</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  holds <br/>(  not <font color="Olive" title="b6">v1</font>,<font color="Olive" title="b7">w1</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> or ( not <font color="Olive" title="b6">v1</font>,<font color="Olive" title="b7">w1</font>,<font color="Olive" title="b3">u</font>,<font color="Olive" title="b5">w</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; not <font color="Olive" title="b6">v1</font>,<font color="Olive" title="b7">w1</font>,<font color="Olive" title="b5">w</font>,<font color="Olive" title="b3">u</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> ) or <font color="Olive" title="b6">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">w1</font> ) ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</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> implies  ex <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</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">u</font>,<font color="Olive" title="b2">v</font>,<font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">w</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; ( for <font color="Olive" title="b4">v1</font>, <font color="Olive" title="b5">w1</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  holds <br/>(  not <font color="Olive" title="b4">v1</font>,<font color="Olive" title="b5">w1</font>,<font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">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> or ( not <font color="Olive" title="b4">v1</font>,<font color="Olive" title="b5">w1</font>,<font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">w</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; not <font color="Olive" title="b4">v1</font>,<font color="Olive" title="b5">w1</font>,<font color="Olive" title="b3">w</font>,<font color="Olive" title="b1">u</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> ) or <font color="Olive" title="b4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">w1</font> ) ) ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:64"/><span class="lab"><font color="Green" title="E32">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">  ex <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</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">u</font>,<font color="Olive" title="b2">v</font>,<font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">w</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; ( for <font color="Olive" title="b4">v1</font>, <font color="Olive" title="b5">w1</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  holds <br/>(  not <font color="Olive" title="b4">v1</font>,<font color="Olive" title="b5">w1</font>,<font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">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> or ( not <font color="Olive" title="b4">v1</font>,<font color="Olive" title="b5">w1</font>,<font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">w</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; not <font color="Olive" title="b4">v1</font>,<font color="Olive" title="b5">w1</font>,<font color="Olive" title="b3">w</font>,<font color="Olive" title="b1">u</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> ) or <font color="Olive" title="b4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">w1</font> ) ) )</span><br/>

<span class="kw">take </span><font color="Maroon" title="c4">u</font> = <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="analort.html#K1" title="ANALORT:func.1">+</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</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="Maroon" title="c4">u</font>,<font color="Olive" title="b1">v</font>,<font color="Maroon" title="c4">u</font>,<font color="Olive" title="b2">w</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; ( for <font color="Olive" title="b3">v1</font>, <font color="Olive" title="b4">w1</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  holds <br/>(  not <font color="Olive" title="b3">v1</font>,<font color="Olive" title="b4">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Olive" title="b1">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> or ( not <font color="Olive" title="b3">v1</font>,<font color="Olive" title="b4">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Olive" title="b2">w</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; not <font color="Olive" title="b3">v1</font>,<font color="Olive" title="b4">w1</font>,<font color="Olive" title="b2">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Olive" title="b3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">w1</font> ) ) )</span><br/>

<span class="kw">take </span><font color="Maroon" title="c5">v</font> = <span class="p1">(<span class="default">1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="analort.html#K1" title="ANALORT:func.1">+</a> <span class="p1">(<span class="default">1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">w</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="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font>,<font color="Olive" title="b1">w</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; ( for <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">w1</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  holds <br/>(  not <font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">w1</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> or ( not <font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Olive" title="b1">w</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; not <font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">w1</font>,<font color="Olive" title="b1">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Olive" title="b2">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">w1</font> ) ) )</span><br/>

<span class="kw">take </span><font color="Maroon" title="c6">w</font> = <span class="p1">(<span class="default">1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="analort.html#K1" title="ANALORT:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span>; <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">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; ( for <font color="Olive" title="b1">v1</font>, <font color="Olive" title="b2">w1</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  holds <br/>(  not <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">w1</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> or ( not <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; not <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Olive" title="b1">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">w1</font> ) ) )</span><br/>

<a NAME="E2:64"/><span class="lab"><font color="Green" title="E33">A2</font></span>: 
 <a href="geomtrap.html#K2" title="GEOMTRAP:func.2">pr1</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="analort.html#E6"><span class="lab"><font color="Green" title="E6">Lm6</font></span></a></span>;<br/>
<a NAME="E3:64"/><span class="lab"><font color="Green" title="E34">A3</font></span>: 
 <a href="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="analort.html#E6"><span class="lab"><font color="Green" title="E6">Lm6</font></span></a></span>;<br/>
<a NAME="E4:64"/><span class="lab"><font color="Green" title="E35">A4</font></span>: 
 <a href="geomtrap.html#K2" title="GEOMTRAP:func.2">pr1</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="analort.html#E6"><span class="lab"><font color="Green" title="E6">Lm6</font></span></a></span>;<br/>
<a NAME="E5:64"/>
 <a href="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="analort.html#E6"><span class="lab"><font color="Green" title="E6">Lm6</font></span></a></span>;<br/>
<a NAME="E6:64"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A5</font></span>: 
 <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="c4">u</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="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:64"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="txt" href="#E3:64"><span class="lab"><font color="Green" title="E34">A3</font></span></a>, <a class="txt" href="#E4:64"><span class="lab"><font color="Green" title="E35">A4</font></span></a>, <a class="ref" href="analoaf.html#T17" title="ANALOAF:th.17">ANALOAF:17</a></span>;<br/>
<a NAME="E7:64"/>
for <font color="Olive" title="b1">v1</font>, <font color="Olive" title="b2">w1</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  holds <br/>(  not <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">w1</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> or ( not <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; not <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Olive" title="b1">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">w1</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c7">v1</font>, <font color="Maroon" title="c8">w1</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"> (  not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</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> or ( not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">w1</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:64_1"/>
<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</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>
 ; <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="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">w1</font> )</span><br/>

<a NAME="E2:64_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A6</font></span>: 
 <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="c7">v1</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="c8">w1</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:64_1_1"/><span class="lab"><font color="Green" title="E38">A7</font></span>: 
<font color="Maroon" title="c7">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">w1</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="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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> or <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( ( not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">w1</font> ) )</span><br/><span class="kw">assume </span><a NAME="E2:64_1_1"/>
( <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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> or <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( ( not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">w1</font> )</span><br/><a NAME="E3:64_1_1"/><span class="kw">then </span>
(  <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="c7">v1</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="c8">w1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</font> or  <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="c7">v1</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="c8">w1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></span>;<br/><a NAME="E4:64_1_1"/><span class="kw">then </span>
( <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="c4">u</font>,<font color="Maroon" title="c6">w</font> or <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">w</font>,<font color="Maroon" title="c4">u</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="#E2:64_1"><span class="lab"><font color="Green" title="E37">A6</font></span></a>, <a class="txt" href="#E1:64_1_1"><span class="lab"><font color="Green" title="E38">A7</font></span></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></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c10">b</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E6:64_1_1"/><span class="lab"><font color="Green" title="E39">A8</font></span>: 
<font color="Maroon" title="c9">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E7:64_1_1"/><span class="lab"><font color="Green" title="E40">A9</font></span>: 
( <font color="Maroon" title="c9">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c10">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T18" title="ANALMETR:th.18">ANALMETR:18</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c11">a</font> = <font color="Maroon" title="c9">a</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">b</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( ( not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">w1</font> )</span><br/><span class="kw">take </span><font color="Maroon" title="c12">b</font> = <font color="Maroon" title="c10">b</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="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">w1</font> )</span><br/><font color="Maroon" title="c4">u</font> = 
<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> <a href="analort.html#K1" title="ANALORT:func.1">+</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T23" title="RLVECT_1:th.23">RLVECT_1:23</a></span>
<br/>.= 
<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> <a href="analort.html#K1" title="ANALORT:func.1">+</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T23" title="RLVECT_1:th.23">RLVECT_1:23</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#T10" title="RLVECT_1:th.10">RLVECT_1:10</a></span>
;<br/><a NAME="E9:64_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<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></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:64_1_1"><span class="lab"><font color="Green" title="E39">A8</font></span></a>, <a class="ref" href="rlvect_1.html#T26" title="RLVECT_1:th.26">RLVECT_1:26</a></span>;<br/><a NAME="E10:64_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A10</font></span>: 
<font color="Maroon" title="c11">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">w</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T26" title="RLVECT_1:th.26">RLVECT_1:26</a></span>;<br/><div><span class="lab"><font color="Green" title="E42">A11</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:64_1_1_2"/><span class="lab"><font color="Green" title="E43">A12</font></span>: 
<font color="Maroon" title="c11">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <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="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">w1</font> )</span><br/><a NAME="E2:64_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">w</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:64_1_1"><span class="lab"><font color="Green" title="E41">A10</font></span></a>, <a class="ref" href="rlvect_1.html#D10" title="RLVECT_1:def.10">RLVECT_1:def 10</a>, <a class="ref" href="rlvect_1.html#D11" title="RLVECT_1:def.11">RLVECT_1:def 11</a></span>;<br/><a NAME="E3:64_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">w</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D10" title="RLVECT_1:def.10">RLVECT_1:def 10</a>, <a class="ref" href="rlvect_1.html#D11" title="RLVECT_1:def.11">RLVECT_1:def 11</a></span>;<br/><a NAME="E4:64_1_1_2"/><span class="kw">then </span>
1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">w</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1_1_2"><span class="lab"><font color="Green" title="E43">A12</font></span></a>, <a class="ref" href="xcmplx_0.html#D7" title="XCMPLX_0:def.7">XCMPLX_0:def 7</a></span>;<br/><a NAME="E5:64_1_1_2"/><span class="kw">then </span>
1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="analort.html#K1" title="ANALORT:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">b</font></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_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="analort.html#E2"><span class="lab"><font color="Green" title="E2">Lm2</font></span></a></span>;<br/><a NAME="E6:64_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A13</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="analort.html#K1" title="ANALORT:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="analort.html#K1" title="ANALORT:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">b</font></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_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="analort.html#E2"><span class="lab"><font color="Green" title="E2">Lm2</font></span></a></span>;<br/><a NAME="E7:64_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="analort.html#E3"><span class="lab"><font color="Green" title="E3">Lm3</font></span></a></span>;<br/><a NAME="E8:64_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A14</font></span>: 
<font color="Maroon" title="c11">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span>
 ;<br/><a NAME="E9:64_1_1_2"/>
1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="#E6:64_1_1_2"><span class="lab"><font color="Green" title="E44">A13</font></span></a>, <a class="txt" href="analort.html#E3"><span class="lab"><font color="Green" title="E3">Lm3</font></span></a></span>;<br/><a NAME="E10:64_1_1_2"/><span class="kw">then </span>
1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1_1_2"><span class="lab"><font color="Green" title="E43">A12</font></span></a>, <a class="txt" href="#E8:64_1_1_2"><span class="lab"><font color="Green" title="E45">A14</font></span></a>, <a class="ref" href="xcmplx_0.html#D7" title="XCMPLX_0:def.7">XCMPLX_0:def 7</a></span>;<br/><span class="kw">hence </span><a NAME="E11:64_1_1_2"/>
( ( not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">w1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1_1_2"><span class="lab"><font color="Green" title="E43">A12</font></span></a>, <a class="ref" href="xcmplx_0.html#D7" title="XCMPLX_0:def.7">XCMPLX_0:def 7</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="64_1_1_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:64_1_1_3"/><span class="lab"><font color="Green" title="E43">A15</font></span>: 
<font color="Maroon" title="c12">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <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="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">w1</font> )</span><br/><a NAME="E2:64_1_1_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">w</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:64_1_1"><span class="lab"><font color="Green" title="E41">A10</font></span></a>, <a class="ref" href="rlvect_1.html#D10" title="RLVECT_1:def.10">RLVECT_1:def 10</a>, <a class="ref" href="rlvect_1.html#D11" title="RLVECT_1:def.11">RLVECT_1:def 11</a></span>;<br/><a NAME="E3:64_1_1_3"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">w</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D10" title="RLVECT_1:def.10">RLVECT_1:def 10</a>, <a class="ref" href="rlvect_1.html#D11" title="RLVECT_1:def.11">RLVECT_1:def 11</a></span>;<br/><a NAME="E4:64_1_1_3"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">w</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1_1_3"><span class="lab"><font color="Green" title="E43">A15</font></span></a>, <a class="ref" href="xcmplx_0.html#D7" title="XCMPLX_0:def.7">XCMPLX_0:def 7</a></span>;<br/><a NAME="E5:64_1_1_3"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="analort.html#K1" title="ANALORT:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">w</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="analort.html#E2"><span class="lab"><font color="Green" title="E2">Lm2</font></span></a></span>;<br/><a NAME="E6:64_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A16</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="analort.html#K1" title="ANALORT:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="analort.html#K1" title="ANALORT:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <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_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="analort.html#E2"><span class="lab"><font color="Green" title="E2">Lm2</font></span></a></span>;<br/><a NAME="E7:64_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c12">b</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="analort.html#E3"><span class="lab"><font color="Green" title="E3">Lm3</font></span></a></span>;<br/><a NAME="E8:64_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A17</font></span>: 
<font color="Maroon" title="c12">b</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span>
 ;<br/><a NAME="E9:64_1_1_3"/>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="#E6:64_1_1_3"><span class="lab"><font color="Green" title="E44">A16</font></span></a>, <a class="txt" href="analort.html#E3"><span class="lab"><font color="Green" title="E3">Lm3</font></span></a></span>;<br/><a NAME="E10:64_1_1_3"/><span class="kw">then </span>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1_1_3"><span class="lab"><font color="Green" title="E43">A15</font></span></a>, <a class="txt" href="#E8:64_1_1_3"><span class="lab"><font color="Green" title="E45">A17</font></span></a>, <a class="ref" href="xcmplx_0.html#D7" title="XCMPLX_0:def.7">XCMPLX_0:def 7</a></span>;<br/><span class="kw">hence </span><a NAME="E11:64_1_1_3"/>
( ( not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">w1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1_1_3"><span class="lab"><font color="Green" title="E43">A15</font></span></a>, <a class="ref" href="xcmplx_0.html#D7" title="XCMPLX_0:def.7">XCMPLX_0:def 7</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="E13:64_1_1"/>
( ( not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">w1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:64_1_1"><span class="lab"><font color="Green" title="E40">A9</font></span></a>, <a class="txt" href="#E11:64_1_1"><span class="lab"><font color="Green" title="E42">A11</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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:64_1"/>
( ( not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; not <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">w1</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/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E8:64"/>
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; ( for <font color="Olive" title="b1">v1</font>, <font color="Olive" title="b2">w1</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  holds <br/>(  not <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">w1</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> or ( not <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">w1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">w</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; not <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">w1</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">u</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> ) or <font color="Olive" title="b1">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">w1</font> ) ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:64"><span class="lab"><font color="Green" title="E36">A5</font></span></a>, <a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</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>
