<?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">OAS</font> being  <a href="analoaf.html#NM1" title="ANALOAF:NM.1">OAffinSpace</a>  st <font color="Olive" title="b1">OAS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <font color="Maroon" title="c1">V</font> holds <br/> <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Olive" title="b1">OAS</font> is  <a href="aff_2.html#V2" title="AFF_2:attr.2">Pappian</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">OAS</font> be   <a href="analoaf.html#NM1" title="ANALOAF:NM.1">OAffinSpace</a>; <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="c2">OAS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <font color="Maroon" title="c1">V</font> implies  <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c2">OAS</font> is  <a href="aff_2.html#V2" title="AFF_2:attr.2">Pappian</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:27"/><span class="lab"><font color="Green" title="E22">A1</font></span>: 
<font color="Maroon" title="c2">OAS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <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="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c2">OAS</font> is  <a href="aff_2.html#V2" title="AFF_2:attr.2">Pappian</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">AS</font> =  <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c2">OAS</font>;<br/>
<a NAME="E2:27"/>
for <font color="Olive" title="b1">M</font>, <font color="Olive" title="b2">N</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c2">OAS</font></span>)</span><br/> for <font color="Olive" title="b3">o</font>, <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</font>, <font color="Olive" title="b6">c</font>, <font color="Olive" title="b7">a9</font>, <font color="Olive" title="b8">b9</font>, <font color="Olive" title="b9">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c2">OAS</font></span>)</span>  st <font color="Olive" title="b1">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Olive" title="b2">N</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Olive" title="b1">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">N</font> &amp; <font color="Olive" title="b3">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b3">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Olive" title="b3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">a</font> &amp; <font color="Olive" title="b3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b7">a9</font> &amp; <font color="Olive" title="b3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">b</font> &amp; <font color="Olive" title="b3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b8">b9</font> &amp; <font color="Olive" title="b3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">c</font> &amp; <font color="Olive" title="b3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b9">c9</font> &amp; <font color="Olive" title="b4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b7">a9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Olive" title="b8">b9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Olive" title="b9">c9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Olive" title="b4">a</font>,<font color="Olive" title="b8">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b</font>,<font color="Olive" title="b7">a9</font> &amp; <font color="Olive" title="b5">b</font>,<font color="Olive" title="b9">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">c</font>,<font color="Olive" title="b8">b9</font> holds <br/><font color="Olive" title="b4">a</font>,<font color="Olive" title="b9">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">c</font>,<font color="Olive" title="b7">a9</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">M</font>, <font color="Maroon" title="c5">N</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c2">OAS</font></span>)</span>; <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">o</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">a9</font>, <font color="Olive" title="b6">b9</font>, <font color="Olive" title="b7">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c2">OAS</font></span>)</span>  st <font color="Maroon" title="c4">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c5">N</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c4">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">N</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">N</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">a</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">a9</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">b9</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">c</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b7">c9</font> &amp; <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Olive" title="b3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Olive" title="b4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Olive" title="b5">a9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">N</font> &amp; <font color="Olive" title="b6">b9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">N</font> &amp; <font color="Olive" title="b7">c9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">N</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b6">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">a9</font> &amp; <font color="Olive" title="b3">b</font>,<font color="Olive" title="b7">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">c</font>,<font color="Olive" title="b6">b9</font> holds <br/><font color="Olive" title="b2">a</font>,<font color="Olive" title="b7">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">a9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">o</font>, <font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">b</font>, <font color="Maroon" title="c9">c</font>, <font color="Maroon" title="c10">a9</font>, <font color="Maroon" title="c11">b9</font>, <font color="Maroon" title="c12">c9</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c2">OAS</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">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c5">N</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c4">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">N</font> &amp; <font color="Maroon" title="c6">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c6">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">N</font> &amp; <font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">a</font> &amp; <font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">a9</font> &amp; <font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b</font> &amp; <font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">b9</font> &amp; <font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">c</font> &amp; <font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">c9</font> &amp; <font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c8">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c9">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c10">a9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">N</font> &amp; <font color="Maroon" title="c11">b9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">N</font> &amp; <font color="Maroon" title="c12">c9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">N</font> &amp; <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c10">a9</font> &amp; <font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c12">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c11">b9</font> implies <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c12">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">a9</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:27_1"/><span class="lab"><font color="Green" title="E23">A2</font></span>: 
<font color="Maroon" title="c4">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E2:27_1"/><span class="lab"><font color="Green" title="E24">A3</font></span>: 
<font color="Maroon" title="c5">N</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E3:27_1"/><span class="lab"><font color="Green" title="E25">A4</font></span>: 
<font color="Maroon" title="c4">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">N</font>
 <span class="kw">and </span><br/><a NAME="E4:27_1"/><span class="lab"><font color="Green" title="E26">A5</font></span>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font>
 <span class="kw">and </span><br/><a NAME="E5:27_1"/><span class="lab"><font color="Green" title="E27">A6</font></span>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">N</font>
 <span class="kw">and </span><br/><a NAME="E6:27_1"/><span class="lab"><font color="Green" title="E28">A7</font></span>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">a</font>
 <span class="kw">and </span><br/><a NAME="E7:27_1"/><span class="lab"><font color="Green" title="E29">A8</font></span>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">a9</font>
 <span class="kw">and </span><br/><a NAME="E8:27_1"/><span class="lab"><font color="Green" title="E30">A9</font></span>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b</font>
 <span class="kw">and </span><br/><a NAME="E9:27_1"/>
<font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">b9</font>
 <span class="kw">and </span><br/><a NAME="E10:27_1"/><span class="lab"><font color="Green" title="E31">A10</font></span>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">c</font>
 <span class="kw">and </span><br/><a NAME="E11:27_1"/><span class="lab"><font color="Green" title="E32">A11</font></span>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">c9</font>
 <span class="kw">and </span><br/><a NAME="E12:27_1"/><span class="lab"><font color="Green" title="E33">A12</font></span>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font>
 <span class="kw">and </span><br/><a NAME="E13:27_1"/><span class="lab"><font color="Green" title="E34">A13</font></span>: 
<font color="Maroon" title="c8">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font>
 <span class="kw">and </span><br/><a NAME="E14:27_1"/><span class="lab"><font color="Green" title="E35">A14</font></span>: 
<font color="Maroon" title="c9">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font>
 <span class="kw">and </span><br/><a NAME="E15:27_1"/><span class="lab"><font color="Green" title="E36">A15</font></span>: 
<font color="Maroon" title="c10">a9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">N</font>
 <span class="kw">and </span><br/><a NAME="E16:27_1"/><span class="lab"><font color="Green" title="E37">A16</font></span>: 
<font color="Maroon" title="c11">b9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">N</font>
 <span class="kw">and </span><br/><a NAME="E17:27_1"/><span class="lab"><font color="Green" title="E38">A17</font></span>: 
<font color="Maroon" title="c12">c9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">N</font>
 <span class="kw">and </span><br/><a NAME="E18:27_1"/><span class="lab"><font color="Green" title="E39">A18</font></span>: 
<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c10">a9</font>
 <span class="kw">and </span><br/><a NAME="E19:27_1"/><span class="lab"><font color="Green" title="E40">A19</font></span>: 
<font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c12">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c11">b9</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">a</font>,<font color="Maroon" title="c12">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">a9</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c13">o1</font> = <font color="Maroon" title="c6">o</font>, <font color="Maroon" title="c14">a1</font> = <font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c15">b1</font> = <font color="Maroon" title="c8">b</font>, <font color="Maroon" title="c16">c1</font> = <font color="Maroon" title="c9">c</font>, <font color="Maroon" title="c17">a19</font> = <font color="Maroon" title="c10">a9</font>, <font color="Maroon" title="c18">b19</font> = <font color="Maroon" title="c11">b9</font>, <font color="Maroon" title="c19">c19</font> = <font color="Maroon" title="c12">c9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">OAS</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="papdesaf.html#T2" target="_self" title="PAPDESAF:th.2">Th2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c20">q</font> = <font color="Maroon" title="c13">o1</font>, <font color="Maroon" title="c21">u</font> = <font color="Maroon" title="c14">a1</font>, <font color="Maroon" title="c22">v</font> = <font color="Maroon" title="c15">b1</font>, <font color="Maroon" title="c23">w</font> = <font color="Maroon" title="c16">c1</font>, <font color="Maroon" title="c24">u9</font> = <font color="Maroon" title="c17">a19</font>, <font color="Maroon" title="c25">v9</font> = <font color="Maroon" title="c18">b19</font>, <font color="Maroon" title="c26">w9</font> = <font color="Maroon" title="c19">c19</font> as   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="papdesaf.html#T4" target="_self" title="PAPDESAF:th.4">Th4</a></span>;<br/>
<a NAME="E22:27_1"/>
<font color="Maroon" title="c15">b1</font>,<font color="Maroon" title="c19">c19</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c16">c1</font>,<font color="Maroon" title="c18">b19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:27_1"><span class="lab"><font color="Green" title="E40">A19</font></span></a>, <a class="ref" href="diraf.html#T45" title="DIRAF:th.45">DIRAF:45</a></span>;<br/>
<a NAME="E23:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A20</font></span>: 
<font color="Maroon" title="c22">v</font>,<font color="Maroon" title="c26">w9</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c23">w</font>,<font color="Maroon" title="c25">v9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="papdesaf.html#T5" target="_self" title="PAPDESAF:th.5">Th5</a></span>;<br/>
<a NAME="E24:27_1"/><span class="lab"><font color="Green" title="E42">A21</font></span>: 
( not <font color="Maroon" title="c20">q</font>,<font color="Maroon" title="c22">v</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c20">q</font>,<font color="Maroon" title="c26">w9</font> &amp; not <font color="Maroon" title="c20">q</font>,<font color="Maroon" title="c22">v</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c20">q</font>,<font color="Maroon" title="c24">u9</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:27_1_1"/>
( <font color="Maroon" title="c20">q</font>,<font color="Maroon" title="c22">v</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c20">q</font>,<font color="Maroon" title="c26">w9</font> or <font color="Maroon" title="c20">q</font>,<font color="Maroon" title="c22">v</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c20">q</font>,<font color="Maroon" title="c24">u9</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:27_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c13">o1</font>,<font color="Maroon" title="c15">b1</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c13">o1</font>,<font color="Maroon" title="c19">c19</font> or <font color="Maroon" title="c13">o1</font>,<font color="Maroon" title="c15">b1</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c13">o1</font>,<font color="Maroon" title="c17">a19</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="papdesaf.html#T5" target="_self" title="PAPDESAF:th.5">Th5</a></span>;<br/>
<a NAME="E3:27_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c8">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c12">c9</font> or <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c8">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c10">a9</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T45" title="DIRAF:th.45">DIRAF:45</a></span>;<br/>
<a NAME="E4:27_1_1"/><span class="kw">then </span>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c12">c9</font> or  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c10">a9</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E5:27_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c12">c9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> or <font color="Maroon" title="c10">a9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="txt" href="#E4:27_1"><span class="lab"><font color="Green" title="E26">A5</font></span></a>, <a class="txt" href="#E8:27_1"><span class="lab"><font color="Green" title="E30">A9</font></span></a>, <a class="txt" href="#E13:27_1"><span class="lab"><font color="Green" title="E34">A13</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:27_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="txt" href="#E2:27_1"><span class="lab"><font color="Green" title="E24">A3</font></span></a>, <a class="txt" href="#E3:27_1"><span class="lab"><font color="Green" title="E25">A4</font></span></a>, <a class="txt" href="#E4:27_1"><span class="lab"><font color="Green" title="E26">A5</font></span></a>, <a class="txt" href="#E5:27_1"><span class="lab"><font color="Green" title="E27">A6</font></span></a>, <a class="txt" href="#E7:27_1"><span class="lab"><font color="Green" title="E29">A8</font></span></a>, <a class="txt" href="#E11:27_1"><span class="lab"><font color="Green" title="E32">A11</font></span></a>, <a class="txt" href="#E15:27_1"><span class="lab"><font color="Green" title="E36">A15</font></span></a>, <a class="txt" href="#E17:27_1"><span class="lab"><font color="Green" title="E38">A17</font></span></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</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>
<a NAME="E25:27_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c8">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="txt" href="#E4:27_1"><span class="lab"><font color="Green" title="E26">A5</font></span></a>, <a class="txt" href="#E13:27_1"><span class="lab"><font color="Green" title="E34">A13</font></span></a>, <a class="txt" href="#E14:27_1"><span class="lab"><font color="Green" title="E35">A14</font></span></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/>
<a NAME="E26:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c8">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E27:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c13">o1</font>,<font color="Maroon" title="c16">c1</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c13">o1</font>,<font color="Maroon" title="c15">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T45" title="DIRAF:th.45">DIRAF:45</a></span>;<br/>
<a NAME="E28:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">q</font>,<font color="Maroon" title="c23">w</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c20">q</font>,<font color="Maroon" title="c22">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="papdesaf.html#T5" target="_self" title="PAPDESAF:th.5">Th5</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c27">r2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E30:27_1"/><span class="lab"><font color="Green" title="E43">A22</font></span>: 
<font color="Maroon" title="c23">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">r2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E31:27_1"/><span class="lab"><font color="Green" title="E44">A23</font></span>: 
<font color="Maroon" title="c27">r2</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="txt" href="#E8:27_1"><span class="lab"><font color="Green" title="E30">A9</font></span></a>, <a class="txt" href="#E10:27_1"><span class="lab"><font color="Green" title="E31">A10</font></span></a>, <a class="txt" href="papdesaf.html#E36"><span class="lab"><font color="Green" title="E19">Lm2</font></span></a></span>;<br/>
<a NAME="E32:27_1"/><span class="lab"><font color="Green" title="E45">A24</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c27">r2</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="txt" href="#E31:27_1"><span class="lab"><font color="Green" title="E44">A23</font></span></a></span>;<br/>
<a NAME="E33:27_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="txt" href="#E4:27_1"><span class="lab"><font color="Green" title="E26">A5</font></span></a>, <a class="txt" href="#E12:27_1"><span class="lab"><font color="Green" title="E33">A12</font></span></a>, <a class="txt" href="#E13:27_1"><span class="lab"><font color="Green" title="E34">A13</font></span></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/>
<a NAME="E34:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c7">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c8">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E35:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c13">o1</font>,<font color="Maroon" title="c14">a1</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c13">o1</font>,<font color="Maroon" title="c15">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T45" title="DIRAF:th.45">DIRAF:45</a></span>;<br/>
<a NAME="E36:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">q</font>,<font color="Maroon" title="c21">u</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c20">q</font>,<font color="Maroon" title="c22">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="papdesaf.html#T5" target="_self" title="PAPDESAF:th.5">Th5</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c28">r1</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E38:27_1"/><span class="lab"><font color="Green" title="E46">A25</font></span>: 
<font color="Maroon" title="c21">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">r1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E39:27_1"/><span class="lab"><font color="Green" title="E47">A26</font></span>: 
<font color="Maroon" title="c28">r1</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="txt" href="#E6:27_1"><span class="lab"><font color="Green" title="E28">A7</font></span></a>, <a class="txt" href="#E8:27_1"><span class="lab"><font color="Green" title="E30">A9</font></span></a>, <a class="txt" href="papdesaf.html#E36"><span class="lab"><font color="Green" title="E19">Lm2</font></span></a></span>;<br/>
<span class="lab"><font color="Green" title="E48">A27</font></span>: <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c28">r1</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c20">q</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c22">v</font></span>)</span> = 
<font color="Maroon" title="c28">r1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c20">q</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c22">v</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T38" title="RLVECT_1:th.38">RLVECT_1:38</a></span>
<br/>.= 
<font color="Maroon" title="c21">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:27_1"><span class="lab"><font color="Green" title="E46">A25</font></span></a>, <a class="ref" href="rlvect_1.html#T47" title="RLVECT_1:th.47">RLVECT_1:47</a></span>
;<br/>
<a NAME="E41:27_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c12">c9</font>,<font color="Maroon" title="c11">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27_1"><span class="lab"><font color="Green" title="E24">A3</font></span></a>, <a class="txt" href="#E5:27_1"><span class="lab"><font color="Green" title="E27">A6</font></span></a>, <a class="txt" href="#E16:27_1"><span class="lab"><font color="Green" title="E37">A16</font></span></a>, <a class="txt" href="#E17:27_1"><span class="lab"><font color="Green" title="E38">A17</font></span></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/>
<a NAME="E42:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c12">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c11">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E43:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c13">o1</font>,<font color="Maroon" title="c19">c19</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c13">o1</font>,<font color="Maroon" title="c18">b19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T45" title="DIRAF:th.45">DIRAF:45</a></span>;<br/>
<a NAME="E44:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A28</font></span>: 
<font color="Maroon" title="c20">q</font>,<font color="Maroon" title="c26">w9</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c20">q</font>,<font color="Maroon" title="c25">v9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="papdesaf.html#T5" target="_self" title="PAPDESAF:th.5">Th5</a></span>;<br/>
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c27">r2</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c20">q</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c22">v</font></span>)</span> = 
<font color="Maroon" title="c27">r2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c20">q</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c22">v</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T38" title="RLVECT_1:th.38">RLVECT_1:38</a></span>
<br/>.= 
<font color="Maroon" title="c23">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:27_1"><span class="lab"><font color="Green" title="E43">A22</font></span></a>, <a class="ref" href="rlvect_1.html#T47" title="RLVECT_1:th.47">RLVECT_1:47</a></span>
;<br/>
<a NAME="E46:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A29</font></span>: 
<font color="Maroon" title="c20">q</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c22">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.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> <font color="Maroon" title="c27">r2</font></span>)</span> <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="c23">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:27_1"><span class="lab"><font color="Green" title="E45">A24</font></span></a>, <a class="ref" href="analoaf.html#T12" title="ANALOAF:th.12">ANALOAF:12</a></span>;<br/>
<a NAME="E47:27_1"/>
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c27">r2</font></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a>  <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="txt" href="#E32:27_1"><span class="lab"><font color="Green" title="E45">A24</font></span></a>, <a class="ref" href="xcmplx_1.html#T203" title="XCMPLX_1:th.203">XCMPLX_1:203</a></span>;<br/>
<span class="kw">then </span><font color="Maroon" title="c25">v9</font> = 
<font color="Maroon" title="c20">q</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c27">r2</font></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span> <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="p2">(<span class="default"><font color="Maroon" title="c26">w9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:27_1"><span class="lab"><font color="Green" title="E41">A20</font></span></a>, <a class="txt" href="#E46:27_1"><span class="lab"><font color="Green" title="E50">A29</font></span></a>, <a class="txt" href="#E44:27_1"><span class="lab"><font color="Green" title="E49">A28</font></span></a>, <a class="txt" href="#E24:27_1"><span class="lab"><font color="Green" title="E42">A21</font></span></a>, <a class="ref" href="papdesaf.html#T15" target="_self" title="PAPDESAF:th.15">Th15</a></span>
<br/>.= 
<font color="Maroon" title="c20">q</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c27">r2</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span></span>)</span> <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="p2">(<span class="default"><font color="Maroon" title="c26">w9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T224" title="XCMPLX_1:th.224">XCMPLX_1:224</a></span>
<br/>.= 
<font color="Maroon" title="c20">q</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c27">r2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c26">w9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span></span>)</span>

;<br/>
<a NAME="E49:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A30</font></span>: 
<font color="Maroon" title="c25">v9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">r2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c26">w9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlsub_2.html#T78" title="RLSUB_2:th.78">RLSUB_2:78</a></span>;<br/>
<a NAME="E50:27_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c10">a9</font>,<font color="Maroon" title="c11">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27_1"><span class="lab"><font color="Green" title="E24">A3</font></span></a>, <a class="txt" href="#E5:27_1"><span class="lab"><font color="Green" title="E27">A6</font></span></a>, <a class="txt" href="#E15:27_1"><span class="lab"><font color="Green" title="E36">A15</font></span></a>, <a class="txt" href="#E16:27_1"><span class="lab"><font color="Green" title="E37">A16</font></span></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/>
<a NAME="E51:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c10">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c11">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E52:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c13">o1</font>,<font color="Maroon" title="c17">a19</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c13">o1</font>,<font color="Maroon" title="c18">b19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T45" title="DIRAF:th.45">DIRAF:45</a></span>;<br/>
<a NAME="E53:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A31</font></span>: 
<font color="Maroon" title="c20">q</font>,<font color="Maroon" title="c24">u9</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c20">q</font>,<font color="Maroon" title="c25">v9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="papdesaf.html#T5" target="_self" title="PAPDESAF:th.5">Th5</a></span>;<br/>
<a NAME="E54:27_1"/>
<font color="Maroon" title="c14">a1</font>,<font color="Maroon" title="c18">b19</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c15">b1</font>,<font color="Maroon" title="c17">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:27_1"><span class="lab"><font color="Green" title="E39">A18</font></span></a>, <a class="ref" href="diraf.html#T45" title="DIRAF:th.45">DIRAF:45</a></span>;<br/>
<a NAME="E55:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">b1</font>,<font color="Maroon" title="c17">a19</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c14">a1</font>,<font color="Maroon" title="c18">b19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a></span>;<br/>
<a NAME="E56:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A32</font></span>: 
<font color="Maroon" title="c22">v</font>,<font color="Maroon" title="c24">u9</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c21">u</font>,<font color="Maroon" title="c25">v9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="papdesaf.html#T5" target="_self" title="PAPDESAF:th.5">Th5</a></span>;<br/>
<a NAME="E57:27_1"/>
<font color="Maroon" title="c28">r1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a>  <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="txt" href="#E39:27_1"><span class="lab"><font color="Green" title="E47">A26</font></span></a>, <a class="ref" href="xcmplx_1.html#T203" title="XCMPLX_1:th.203">XCMPLX_1:203</a></span>;<br/>
<a NAME="E58:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A33</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c28">r1</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="c27">r2</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="txt" href="#E31:27_1"><span class="lab"><font color="Green" title="E44">A23</font></span></a>, <a class="ref" href="xcmplx_1.html#T6" title="XCMPLX_1:th.6">XCMPLX_1:6</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c29">s</font> = <font color="Maroon" title="c28">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c27">r2</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span>;<br/>
<span class="lab"><font color="Green" title="E55">A34</font></span>: <font color="Maroon" title="c21">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font> = 
<font color="Maroon" title="c28">r1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c27">r2</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="p2">(<span class="default"><font color="Maroon" title="c23">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:27_1"><span class="lab"><font color="Green" title="E46">A25</font></span></a>, <a class="txt" href="#E30:27_1"><span class="lab"><font color="Green" title="E43">A22</font></span></a>, <a class="txt" href="#E31:27_1"><span class="lab"><font color="Green" title="E44">A23</font></span></a>, <a class="ref" href="analoaf.html#T13" title="ANALOAF:th.13">ANALOAF:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c28">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">r2</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span>
<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="E60:27_1"/>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c28">r1</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="txt" href="#E39:27_1"><span class="lab"><font color="Green" title="E47">A26</font></span></a></span>;<br/>
<a NAME="E61:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A35</font></span>: 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c28">r1</font></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a>  <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="xcmplx_1.html#T203" title="XCMPLX_1:th.203">XCMPLX_1:203</a></span>;<br/>
<a NAME="E62:27_1"/>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c28">r1</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="txt" href="#E39:27_1"><span class="lab"><font color="Green" title="E47">A26</font></span></a></span>;<br/>
<a NAME="E63:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">q</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c22">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.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> <font color="Maroon" title="c28">r1</font></span>)</span> <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="c21">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:27_1"><span class="lab"><font color="Green" title="E48">A27</font></span></a>, <a class="ref" href="analoaf.html#T13" title="ANALOAF:th.13">ANALOAF:13</a></span>;<br/>
<span class="kw">then </span><font color="Maroon" title="c25">v9</font> = 
<font color="Maroon" title="c20">q</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c28">r1</font></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span> <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="p2">(<span class="default"><font color="Maroon" title="c24">u9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:27_1"><span class="lab"><font color="Green" title="E53">A32</font></span></a>, <a class="txt" href="#E61:27_1"><span class="lab"><font color="Green" title="E56">A35</font></span></a>, <a class="txt" href="#E53:27_1"><span class="lab"><font color="Green" title="E52">A31</font></span></a>, <a class="txt" href="#E24:27_1"><span class="lab"><font color="Green" title="E42">A21</font></span></a>, <a class="ref" href="papdesaf.html#T15" target="_self" title="PAPDESAF:th.15">Th15</a></span>
<br/>.= 
<font color="Maroon" title="c20">q</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c28">r1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span></span>)</span> <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="p2">(<span class="default"><font color="Maroon" title="c24">u9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T224" title="XCMPLX_1:th.224">XCMPLX_1:224</a></span>
<br/>.= 
<font color="Maroon" title="c20">q</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c28">r1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">u9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span></span>)</span>

;<br/>
<a NAME="E65:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c25">v9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">r1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">u9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlsub_2.html#T78" title="RLSUB_2:th.78">RLSUB_2:78</a></span>;<br/>
<span class="kw">then </span><font color="Maroon" title="c24">u9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c28">r1</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="c27">r2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c26">w9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:27_1"><span class="lab"><font color="Green" title="E47">A26</font></span></a>, <a class="txt" href="#E49:27_1"><span class="lab"><font color="Green" title="E51">A30</font></span></a>, <a class="ref" href="analoaf.html#T13" title="ANALOAF:th.13">ANALOAF:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c28">r1</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="c27">r2</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c26">w9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span>
<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/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E57">A36</font></span>: <font color="Maroon" title="c26">w9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c28">r1</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="c27">r2</font></span>)</span> <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="c24">u9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E58:27_1"><span class="lab"><font color="Green" title="E54">A33</font></span></a>, <a class="ref" href="analoaf.html#T13" title="ANALOAF:th.13">ANALOAF:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c28">r1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <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="c27">r2</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">u9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T205" title="XCMPLX_1:th.205">XCMPLX_1:205</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c28">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">r2</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">u9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span>

;<br/>
1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c26">w9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c21">u</font></span>)</span> = 
<font color="Maroon" title="c26">w9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c21">u</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D11" title="RLVECT_1:def.11">RLVECT_1:def 11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c28">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c27">r2</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">u9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c28">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c27">r2</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c23">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E67:27_1"><span class="lab"><font color="Green" title="E57">A36</font></span></a>, <a class="txt" href="#E59:27_1"><span class="lab"><font color="Green" title="E55">A34</font></span></a>, <a class="txt" href="papdesaf.html#E37"><span class="lab"><font color="Green" title="E20">Lm3</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c28">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">r2</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">u9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c23">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T48" title="RLVECT_1:th.48">RLVECT_1:48</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c28">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">r2</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">u9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c23">w</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="papdesaf.html#E37"><span class="lab"><font color="Green" title="E20">Lm3</font></span></a></span>
;<br/>
<a NAME="E69:27_1"/><span class="kw">then </span>
( <font color="Maroon" title="c21">u</font>,<font color="Maroon" title="c26">w9</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c23">w</font>,<font color="Maroon" title="c24">u9</font> or <font color="Maroon" title="c21">u</font>,<font color="Maroon" title="c26">w9</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c24">u9</font>,<font color="Maroon" title="c23">w</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T18" title="ANALMETR:th.18">ANALMETR:18</a></span>;<br/>
<a NAME="E70:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c21">u</font>,<font color="Maroon" title="c26">w9</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c23">w</font>,<font color="Maroon" title="c24">u9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="geomtrap.html#D1" title="GEOMTRAP:def.1">GEOMTRAP:def 1</a></span>;<br/>
<a NAME="E71:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">a1</font>,<font color="Maroon" title="c19">c19</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c16">c1</font>,<font color="Maroon" title="c17">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="papdesaf.html#T5" target="_self" title="PAPDESAF:th.5">Th5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E72:27_1"/>
<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c12">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T45" title="DIRAF:th.45">DIRAF:45</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="E3:27"/>
 <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c2">OAS</font> is  <a href="aff_2.html#V2" title="AFF_2:attr.2">Pappian</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_2.html#D2" title="AFF_2:def.2">AFF_2:def 2</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>
