<?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">o</font>, <font color="Olive" title="b2">u</font>, <font color="Olive" title="b3">v</font>, <font color="Olive" title="b4">w</font>, <font color="Olive" title="b5">u2</font>, <font color="Olive" title="b6">v2</font>, <font color="Olive" title="b7">w2</font>, <font color="Olive" title="b8">u1</font>, <font color="Olive" title="b9">v1</font>, <font color="Olive" title="b10">w1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font>  st not <font color="Olive" title="b1">o</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  &amp; <font color="Olive" title="b2">u</font>,<font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">w</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a>  &amp; <font color="Olive" title="b5">u2</font>,<font color="Olive" title="b6">v2</font>,<font color="Olive" title="b7">w2</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a>  &amp; <font color="Olive" title="b8">u1</font>,<font color="Olive" title="b9">v1</font>,<font color="Olive" title="b10">w1</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">u</font>,<font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">w</font>,<font color="Olive" title="b5">u2</font>,<font color="Olive" title="b6">v2</font>,<font color="Olive" title="b7">w2</font> <a href="anproj_2.html#R4" title="ANPROJ_2:pred.4">lie_on_an_angle</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">u</font>,<font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">w</font>,<font color="Olive" title="b5">u2</font>,<font color="Olive" title="b6">v2</font>,<font color="Olive" title="b7">w2</font> <a href="anproj_2.html#R5" title="ANPROJ_2:pred.5">are_half_mutually_not_Prop</a>  &amp; <font color="Olive" title="b2">u</font>,<font color="Olive" title="b6">v2</font>,<font color="Olive" title="b10">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Olive" title="b5">u2</font>,<font color="Olive" title="b3">v</font>,<font color="Olive" title="b10">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Olive" title="b2">u</font>,<font color="Olive" title="b7">w2</font>,<font color="Olive" title="b9">v1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Olive" title="b4">w</font>,<font color="Olive" title="b5">u2</font>,<font color="Olive" title="b9">v1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Olive" title="b3">v</font>,<font color="Olive" title="b7">w2</font>,<font color="Olive" title="b8">u1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Olive" title="b4">w</font>,<font color="Olive" title="b6">v2</font>,<font color="Olive" title="b8">u1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  holds <br/><font color="Olive" title="b8">u1</font>,<font color="Olive" title="b9">v1</font>,<font color="Olive" title="b10">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">u</font>, <font color="Maroon" title="c4">v</font>, <font color="Maroon" title="c5">w</font>, <font color="Maroon" title="c6">u2</font>, <font color="Maroon" title="c7">v2</font>, <font color="Maroon" title="c8">w2</font>, <font color="Maroon" title="c9">u1</font>, <font color="Maroon" title="c10">v1</font>, <font color="Maroon" title="c11">w1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c2">o</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  &amp; <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">w</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a>  &amp; <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c8">w2</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a>  &amp; <font color="Maroon" title="c9">u1</font>,<font color="Maroon" title="c10">v1</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c8">w2</font> <a href="anproj_2.html#R4" title="ANPROJ_2:pred.4">lie_on_an_angle</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c8">w2</font> <a href="anproj_2.html#R5" title="ANPROJ_2:pred.5">are_half_mutually_not_Prop</a>  &amp; <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c8">w2</font>,<font color="Maroon" title="c10">v1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c10">v1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c8">w2</font>,<font color="Maroon" title="c9">u1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c9">u1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  implies <font color="Maroon" title="c9">u1</font>,<font color="Maroon" title="c10">v1</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  )</span><br/>





















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:43"/><span class="lab"><font color="Green" title="E44">A1</font></span>: 
not <font color="Maroon" title="c2">o</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E2:43"/><span class="lab"><font color="Green" title="E45">A2</font></span>: 
<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">w</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 <span class="kw">and </span><br/><a NAME="E3:43"/><span class="lab"><font color="Green" title="E46">A3</font></span>: 
<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c8">w2</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 <span class="kw">and </span><br/><a NAME="E4:43"/><span class="lab"><font color="Green" title="E47">A4</font></span>: 
<font color="Maroon" title="c9">u1</font>,<font color="Maroon" title="c10">v1</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 <span class="kw">and </span><br/><a NAME="E5:43"/><span class="lab"><font color="Green" title="E48">A5</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c8">w2</font> <a href="anproj_2.html#R4" title="ANPROJ_2:pred.4">lie_on_an_angle</a> 
 <span class="kw">and </span><br/><a NAME="E6:43"/><span class="lab"><font color="Green" title="E49">A6</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c8">w2</font> <a href="anproj_2.html#R5" title="ANPROJ_2:pred.5">are_half_mutually_not_Prop</a> 
 <span class="kw">and </span><br/><a NAME="E7:43"/><span class="lab"><font color="Green" title="E50">A7</font></span>: 
<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">and </span><br/><a NAME="E8:43"/><span class="lab"><font color="Green" title="E51">A8</font></span>: 
<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">and </span><br/><a NAME="E9:43"/><span class="lab"><font color="Green" title="E52">A9</font></span>: 
<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c8">w2</font>,<font color="Maroon" title="c10">v1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">and </span><br/><a NAME="E10:43"/><span class="lab"><font color="Green" title="E53">A10</font></span>: 
<font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c10">v1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">and </span><br/><a NAME="E11:43"/><span class="lab"><font color="Green" title="E54">A11</font></span>: 
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c8">w2</font>,<font color="Maroon" title="c9">u1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">and </span><br/><a NAME="E12:43"/><span class="lab"><font color="Green" title="E55">A12</font></span>: 
<font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c9">u1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</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="c9">u1</font>,<font color="Maroon" title="c10">v1</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> </span><br/>

<a NAME="E13:43"/><span class="lab"><font color="Green" title="E56">A13</font></span>: 
not <font color="Maroon" title="c3">u</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E14:43"/><span class="lab"><font color="Green" title="E57">A14</font></span>: 
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:43"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="ref" href="anproj_2.html#D5" target="_self" title="ANPROJ_2:def.5">Def5</a></span>;<br/>
<a NAME="E15:43"/><span class="lab"><font color="Green" title="E58">A15</font></span>: 
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:43"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="ref" href="anproj_2.html#D5" target="_self" title="ANPROJ_2:def.5">Def5</a></span>;<br/>
<a NAME="E16:43"/><span class="lab"><font color="Green" title="E59">A16</font></span>: 
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:43"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="ref" href="anproj_2.html#D5" target="_self" title="ANPROJ_2:def.5">Def5</a></span>;<br/>
<a NAME="E17:43"/><span class="lab"><font color="Green" title="E60">A17</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:43"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="ref" href="anproj_2.html#D4" target="_self" title="ANPROJ_2:def.4">Def4</a></span>;<br/>
<a NAME="E18:43"/><span class="lab"><font color="Green" title="E61">A18</font></span>: 
( not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">w2</font> &amp; not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c8">w2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:43"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="ref" href="anproj_2.html#D5" target="_self" title="ANPROJ_2:def.5">Def5</a></span>;<br/>
<a NAME="E19:43"/><span class="lab"><font color="Green" title="E62">A19</font></span>: 
not <font color="Maroon" title="c6">u2</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E20:43"/><span class="lab"><font color="Green" title="E63">A20</font></span>: 
( not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">w</font> &amp; not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c5">w</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:43"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="ref" href="anproj_2.html#D5" target="_self" title="ANPROJ_2:def.5">Def5</a></span>;<br/>
<a NAME="E21:43"/><span class="lab"><font color="Green" title="E64">A21</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c5">w</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:43"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="ref" href="anproj_2.html#D4" target="_self" title="ANPROJ_2:def.4">Def4</a></span>;<br/>
<a NAME="E22:43"/><span class="lab"><font color="Green" title="E65">A22</font></span>: 
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">v2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:43"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="ref" href="anproj_2.html#D5" target="_self" title="ANPROJ_2:def.5">Def5</a></span>;<br/>
<a NAME="E23:43"/><span class="lab"><font color="Green" title="E66">A23</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c8">w2</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:43"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="ref" href="anproj_2.html#D4" target="_self" title="ANPROJ_2:def.4">Def4</a></span>;<br/>
<a NAME="E24:43"/><span class="lab"><font color="Green" title="E67">A24</font></span>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c6">u2</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:43"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="ref" href="anproj_2.html#D4" target="_self" title="ANPROJ_2:def.4">Def4</a></span>;<br/>
<a NAME="E25:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A25</font></span>: 
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_1.html#T17" title="ANPROJ_1:th.17">ANPROJ_1:17</a></span>;<br/>
<a NAME="E26:43"/><span class="lab"><font color="Green" title="E69">A26</font></span>: 
not <font color="Maroon" title="c5">w</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E27:43"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c5">w</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="txt" href="#E13:43"><span class="lab"><font color="Green" title="E56">A13</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">a3</font>, <font color="Maroon" title="c13">b3</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E29:43"/><span class="lab"><font color="Green" title="E70">A27</font></span>: 
<font color="Maroon" title="c13">b3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E30:43"/>
<font color="Maroon" title="c12">a3</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">and </span><br/><a NAME="E31:43"/><span class="lab"><font color="Green" title="E71">A28</font></span>: 
<font color="Maroon" title="c13">b3</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="#E21:43"><span class="lab"><font color="Green" title="E64">A21</font></span></a>, <a class="txt" href="#E20:43"><span class="lab"><font color="Green" title="E63">A20</font></span></a>, <a class="txt" href="#E25:43"><span class="lab"><font color="Green" title="E68">A25</font></span></a>, <a class="ref" href="anproj_2.html#T6" target="_self" title="ANPROJ_2:th.6">Th6</a></span>;<br/>
<a NAME="E32:43"/><span class="lab"><font color="Green" title="E72">A29</font></span>: 
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:43"><span class="lab"><font color="Green" title="E67">A24</font></span></a>, <a class="ref" href="anproj_1.html#T17" title="ANPROJ_1:th.17">ANPROJ_1:17</a></span>;<br/>
<a NAME="E33:43"/><span class="lab"><font color="Green" title="E73">A30</font></span>: 
not <font color="Maroon" title="c8">w2</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E34:43"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c8">w2</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="txt" href="#E19:43"><span class="lab"><font color="Green" title="E62">A19</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">c3</font>, <font color="Maroon" title="c15">d3</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E36:43"/><span class="lab"><font color="Green" title="E74">A31</font></span>: 
<font color="Maroon" title="c15">d3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c8">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E37:43"/>
<font color="Maroon" title="c14">c3</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">and </span><br/><a NAME="E38:43"/><span class="lab"><font color="Green" title="E75">A32</font></span>: 
<font color="Maroon" title="c15">d3</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="#E23:43"><span class="lab"><font color="Green" title="E66">A23</font></span></a>, <a class="txt" href="#E18:43"><span class="lab"><font color="Green" title="E61">A18</font></span></a>, <a class="txt" href="#E32:43"><span class="lab"><font color="Green" title="E72">A29</font></span></a>, <a class="ref" href="anproj_2.html#T6" target="_self" title="ANPROJ_2:th.6">Th6</a></span>;<br/>
<a NAME="E39:43"/><span class="lab"><font color="Green" title="E76">A33</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:43"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="ref" href="anproj_2.html#D4" target="_self" title="ANPROJ_2:def.4">Def4</a></span>;<br/>
<a NAME="E40:43"/><span class="lab"><font color="Green" title="E77">A34</font></span>: 
not <font color="Maroon" title="c7">v2</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E41:43"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="txt" href="#E19:43"><span class="lab"><font color="Green" title="E62">A19</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c16">c2</font>, <font color="Maroon" title="c17">d2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E43:43"/><span class="lab"><font color="Green" title="E78">A35</font></span>: 
<font color="Maroon" title="c17">d2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c7">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E44:43"/><span class="lab"><font color="Green" title="E79">A36</font></span>: 
<font color="Maroon" title="c16">c2</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">and </span><br/><a NAME="E45:43"/><span class="lab"><font color="Green" title="E80">A37</font></span>: 
<font color="Maroon" title="c17">d2</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="#E17:43"><span class="lab"><font color="Green" title="E60">A17</font></span></a>, <a class="txt" href="#E22:43"><span class="lab"><font color="Green" title="E65">A22</font></span></a>, <a class="txt" href="#E14:43"><span class="lab"><font color="Green" title="E57">A14</font></span></a>, <a class="txt" href="#E32:43"><span class="lab"><font color="Green" title="E72">A29</font></span></a>, <a class="ref" href="anproj_2.html#T6" target="_self" title="ANPROJ_2:th.6">Th6</a></span>;<br/>
<a NAME="E46:43"/><span class="lab"><font color="Green" title="E81">A38</font></span>: 
not <font color="Maroon" title="c4">v</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E47:43"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="txt" href="#E13:43"><span class="lab"><font color="Green" title="E56">A13</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c18">a2</font>, <font color="Maroon" title="c19">b2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E49:43"/><span class="lab"><font color="Green" title="E82">A39</font></span>: 
<font color="Maroon" title="c19">b2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E50:43"/>
<font color="Maroon" title="c18">a2</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">and </span><br/><a NAME="E51:43"/><span class="lab"><font color="Green" title="E83">A40</font></span>: 
<font color="Maroon" title="c19">b2</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="#E39:43"><span class="lab"><font color="Green" title="E76">A33</font></span></a>, <a class="txt" href="#E15:43"><span class="lab"><font color="Green" title="E58">A15</font></span></a>, <a class="txt" href="#E16:43"><span class="lab"><font color="Green" title="E59">A16</font></span></a>, <a class="txt" href="#E25:43"><span class="lab"><font color="Green" title="E68">A25</font></span></a>, <a class="ref" href="anproj_2.html#T6" target="_self" title="ANPROJ_2:th.6">Th6</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c20">v9</font> = <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c21">w9</font> = <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c22">v29</font> = <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c23">w29</font> = <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>;<br/>
<a NAME="E52:43"/><span class="lab"><font color="Green" title="E84">A41</font></span>: 
not <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:43"><span class="lab"><font color="Green" title="E77">A34</font></span></a>, <a class="txt" href="#E43:43"><span class="lab"><font color="Green" title="E78">A35</font></span></a>, <a class="txt" href="#E45:43"><span class="lab"><font color="Green" title="E80">A37</font></span></a>, <a class="txt" href="anproj_2.html#E33"><span class="lab"><font color="Green" title="E33">Lm20</font></span></a></span>;<br/>
<a NAME="E53:43"/><span class="lab"><font color="Green" title="E85">A42</font></span>: 
not <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E46:43"><span class="lab"><font color="Green" title="E81">A38</font></span></a>, <a class="txt" href="#E49:43"><span class="lab"><font color="Green" title="E82">A39</font></span></a>, <a class="txt" href="#E51:43"><span class="lab"><font color="Green" title="E83">A40</font></span></a>, <a class="txt" href="anproj_2.html#E33"><span class="lab"><font color="Green" title="E33">Lm20</font></span></a></span>;<br/>
<a NAME="E54:43"/><span class="lab"><font color="Green" title="E86">A43</font></span>: 
not <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:43"><span class="lab"><font color="Green" title="E69">A26</font></span></a>, <a class="txt" href="#E29:43"><span class="lab"><font color="Green" title="E70">A27</font></span></a>, <a class="txt" href="#E31:43"><span class="lab"><font color="Green" title="E71">A28</font></span></a>, <a class="txt" href="anproj_2.html#E33"><span class="lab"><font color="Green" title="E33">Lm20</font></span></a></span>;<br/>
<a NAME="E55:43"/><span class="lab"><font color="Green" title="E87">A44</font></span>: 
not <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:43"><span class="lab"><font color="Green" title="E73">A30</font></span></a>, <a class="txt" href="#E36:43"><span class="lab"><font color="Green" title="E74">A31</font></span></a>, <a class="txt" href="#E38:43"><span class="lab"><font color="Green" title="E75">A32</font></span></a>, <a class="txt" href="anproj_2.html#E33"><span class="lab"><font color="Green" title="E33">Lm20</font></span></a></span>;<br/>
<a NAME="E56:43"/><span class="lab"><font color="Green" title="E88">A45</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c8">w2</font>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:43"><span class="lab"><font color="Green" title="E74">A31</font></span></a>, <a class="txt" href="#E38:43"><span class="lab"><font color="Green" title="E75">A32</font></span></a>, <a class="txt" href="anproj_2.html#E29"><span class="lab"><font color="Green" title="E29">Lm16</font></span></a></span>;<br/>
<a NAME="E57:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A46</font></span>: 
<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>,<font color="Maroon" title="c10">v1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:43"><span class="lab"><font color="Green" title="E52">A9</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E58:43"/><span class="lab"><font color="Green" title="E90">A47</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:43"><span class="lab"><font color="Green" title="E82">A39</font></span></a>, <a class="txt" href="#E51:43"><span class="lab"><font color="Green" title="E83">A40</font></span></a>, <a class="txt" href="anproj_2.html#E29"><span class="lab"><font color="Green" title="E29">Lm16</font></span></a></span>;<br/>
<a NAME="E59:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E91">A48</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>,<font color="Maroon" title="c9">u1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:43"><span class="lab"><font color="Green" title="E54">A11</font></span></a>, <a class="txt" href="#E56:43"><span class="lab"><font color="Green" title="E88">A45</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E60:43"/><span class="lab"><font color="Green" title="E92">A49</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:43"><span class="lab"><font color="Green" title="E78">A35</font></span></a>, <a class="txt" href="#E45:43"><span class="lab"><font color="Green" title="E80">A37</font></span></a>, <a class="txt" href="anproj_2.html#E29"><span class="lab"><font color="Green" title="E29">Lm16</font></span></a></span>;<br/>
<a NAME="E61:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E93">A50</font></span>: 
<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>,<font color="Maroon" title="c11">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:43"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E62:43"/><span class="lab"><font color="Green" title="E94">A51</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:43"><span class="lab"><font color="Green" title="E70">A27</font></span></a>, <a class="txt" href="#E31:43"><span class="lab"><font color="Green" title="E71">A28</font></span></a>, <a class="txt" href="anproj_2.html#E29"><span class="lab"><font color="Green" title="E29">Lm16</font></span></a></span>;<br/>
<a NAME="E63:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E95">A52</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>,<font color="Maroon" title="c9">u1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:43"><span class="lab"><font color="Green" title="E55">A12</font></span></a>, <a class="txt" href="#E60:43"><span class="lab"><font color="Green" title="E92">A49</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E64:43"/>
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c7">v2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:43_1"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c7">v2</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="E2:43_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c3">u</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:43"><span class="lab"><font color="Green" title="E60">A17</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:43_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:43"><span class="lab"><font color="Green" title="E67">A24</font></span></a>, <a class="ref" href="anproj_1.html#T10" title="ANPROJ_1:th.10">ANPROJ_1:10</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="E65:43"/><span class="kw">then </span>
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:43"><span class="lab"><font color="Green" title="E78">A35</font></span></a>, <a class="txt" href="#E45:43"><span class="lab"><font color="Green" title="E80">A37</font></span></a>, <a class="txt" href="anproj_2.html#E30"><span class="lab"><font color="Green" title="E30">Lm17</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c24">A3</font>, <font color="Maroon" title="c25">B3</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E67:43"/><span class="lab"><font color="Green" title="E96">A53</font></span>: 
<font color="Maroon" title="c11">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">A3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c25">B3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:43"><span class="lab"><font color="Green" title="E56">A13</font></span></a>, <a class="txt" href="#E61:43"><span class="lab"><font color="Green" title="E93">A50</font></span></a>, <a class="txt" href="#E52:43"><span class="lab"><font color="Green" title="E84">A41</font></span></a>, <a class="ref" href="anproj_1.html#T11" title="ANPROJ_1:th.11">ANPROJ_1:11</a></span>;<br/>
<a NAME="E68:43"/>
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c4">v</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:43_2"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c4">v</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 ; <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="E2:43_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E97">A54</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_1.html#T10" title="ANPROJ_1:th.10">ANPROJ_1:10</a></span>;<br/>
<a NAME="E3:43_2"/>
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c3">u</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c2">o</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:43"><span class="lab"><font color="Green" title="E76">A33</font></span></a>, <a class="ref" href="anproj_1.html#T10" title="ANPROJ_1:th.10">ANPROJ_1:10</a>, <a class="ref" href="anproj_1.html#T16" title="ANPROJ_1:th.16">ANPROJ_1:16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:43_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="txt" href="#E46:43"><span class="lab"><font color="Green" title="E81">A38</font></span></a>, <a class="txt" href="#E24:43"><span class="lab"><font color="Green" title="E67">A24</font></span></a>, <a class="txt" href="#E15:43"><span class="lab"><font color="Green" title="E58">A15</font></span></a>, <a class="txt" href="#E2:43_2"><span class="lab"><font color="Green" title="E97">A54</font></span></a>, <a class="ref" href="anproj_1.html#T19" title="ANPROJ_1:th.19">ANPROJ_1:19</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="E69:43"/><span class="kw">then </span>
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c8">w2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:43"><span class="lab"><font color="Green" title="E66">A23</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E70:43"/><span class="kw">then </span>
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:43"><span class="lab"><font color="Green" title="E82">A39</font></span></a>, <a class="txt" href="#E51:43"><span class="lab"><font color="Green" title="E83">A40</font></span></a>, <a class="txt" href="#E36:43"><span class="lab"><font color="Green" title="E74">A31</font></span></a>, <a class="txt" href="#E38:43"><span class="lab"><font color="Green" title="E75">A32</font></span></a>, <a class="txt" href="anproj_2.html#E34"><span class="lab"><font color="Green" title="E34">Lm21</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c26">A1</font>, <font color="Maroon" title="c27">B1</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E72:43"/><span class="lab"><font color="Green" title="E97">A55</font></span>: 
<font color="Maroon" title="c9">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c26">A1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c27">B1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E53:43"><span class="lab"><font color="Green" title="E85">A42</font></span></a>, <a class="txt" href="#E55:43"><span class="lab"><font color="Green" title="E87">A44</font></span></a>, <a class="txt" href="#E59:43"><span class="lab"><font color="Green" title="E91">A48</font></span></a>, <a class="ref" href="anproj_1.html#T11" title="ANPROJ_1:th.11">ANPROJ_1:11</a></span>;<br/>
<a NAME="E73:43"/>
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c7">v2</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:43_3"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c7">v2</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 ; <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="E2:43_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E98">A56</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c3">u</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_1.html#T10" title="ANPROJ_1:th.10">ANPROJ_1:10</a></span>;<br/>
<a NAME="E3:43_3"/>
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c6">u2</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c2">o</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:43"><span class="lab"><font color="Green" title="E60">A17</font></span></a>, <a class="ref" href="anproj_1.html#T10" title="ANPROJ_1:th.10">ANPROJ_1:10</a>, <a class="ref" href="anproj_1.html#T16" title="ANPROJ_1:th.16">ANPROJ_1:16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:43_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="txt" href="#E40:43"><span class="lab"><font color="Green" title="E77">A34</font></span></a>, <a class="txt" href="#E24:43"><span class="lab"><font color="Green" title="E67">A24</font></span></a>, <a class="txt" href="#E22:43"><span class="lab"><font color="Green" title="E65">A22</font></span></a>, <a class="txt" href="#E2:43_3"><span class="lab"><font color="Green" title="E98">A56</font></span></a>, <a class="ref" href="anproj_1.html#T19" title="ANPROJ_1:th.19">ANPROJ_1:19</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="E74:43"/><span class="kw">then </span>
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c5">w</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:43"><span class="lab"><font color="Green" title="E64">A21</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E75:43"/><span class="kw">then </span>
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:43"><span class="lab"><font color="Green" title="E70">A27</font></span></a>, <a class="txt" href="#E31:43"><span class="lab"><font color="Green" title="E71">A28</font></span></a>, <a class="txt" href="#E43:43"><span class="lab"><font color="Green" title="E78">A35</font></span></a>, <a class="txt" href="#E45:43"><span class="lab"><font color="Green" title="E80">A37</font></span></a>, <a class="txt" href="anproj_2.html#E34"><span class="lab"><font color="Green" title="E34">Lm21</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c28">A19</font>, <font color="Maroon" title="c29">B19</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E77:43"/><span class="lab"><font color="Green" title="E98">A57</font></span>: 
<font color="Maroon" title="c9">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c28">A19</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c29">B19</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E52:43"><span class="lab"><font color="Green" title="E84">A41</font></span></a>, <a class="txt" href="#E54:43"><span class="lab"><font color="Green" title="E86">A43</font></span></a>, <a class="txt" href="#E63:43"><span class="lab"><font color="Green" title="E95">A52</font></span></a>, <a class="ref" href="anproj_1.html#T11" title="ANPROJ_1:th.11">ANPROJ_1:11</a></span>;<br/>
<a NAME="E78:43"/><span class="lab"><font color="Green" title="E99">A58</font></span>: 
<font color="Maroon" title="c9">u1</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"><font color="Maroon" title="c26">A1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c27">B1</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c26">A1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">a2</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c27">B1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E72:43"><span class="lab"><font color="Green" title="E97">A55</font></span></a>, <a class="txt" href="anproj_2.html#E35"><span class="lab"><font color="Green" title="E35">Lm22</font></span></a></span>;<br/>
<a NAME="E79:43"/><span class="lab"><font color="Green" title="E100">A59</font></span>: 
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c8">w2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:43"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="ref" href="anproj_2.html#D5" target="_self" title="ANPROJ_2:def.5">Def5</a></span>;<br/>
<a NAME="E80:43"/><span class="lab"><font color="Green" title="E101">A60</font></span>: 
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">w</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:43"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="ref" href="anproj_2.html#D5" target="_self" title="ANPROJ_2:def.5">Def5</a></span>;<br/>
<a NAME="E81:43"/><span class="lab"><font color="Green" title="E102">A61</font></span>: 
( not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> &amp; not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_4"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E103">A62</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_4_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:43_4_1"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 ; <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="E2:43_4_1"/><span class="kw">then </span>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E60:43"><span class="lab"><font color="Green" title="E92">A49</font></span></a>, <a class="ref" href="anproj_1.html#T6" title="ANPROJ_1:th.6">ANPROJ_1:6</a></span>;<br/><span class="kw">hence </span><a NAME="E3:43_4_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E79:43"><span class="lab"><font color="Green" title="E100">A59</font></span></a>, <a class="txt" href="#E56:43"><span class="lab"><font color="Green" title="E88">A45</font></span></a>, <a class="ref" href="anproj_1.html#T6" title="ANPROJ_1:th.6">ANPROJ_1:6</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><span class="lab"><font color="Green" title="E104">A63</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_4_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:43_4_2"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>
 ; <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="E2:43_4_2"/><span class="kw">then </span>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E58:43"><span class="lab"><font color="Green" title="E90">A47</font></span></a>, <a class="ref" href="anproj_1.html#T6" title="ANPROJ_1:th.6">ANPROJ_1:6</a></span>;<br/><span class="kw">hence </span><a NAME="E3:43_4_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E80:43"><span class="lab"><font color="Green" title="E101">A60</font></span></a>, <a class="txt" href="#E62:43"><span class="lab"><font color="Green" title="E94">A51</font></span></a>, <a class="ref" href="anproj_1.html#T6" title="ANPROJ_1:th.6">ANPROJ_1:6</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">assume </span><a NAME="E3:43_4"/>
(  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> or  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:43_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43_4"><span class="lab"><font color="Green" title="E104">A63</font></span></a>, <a class="txt" href="#E1:43_4"><span class="lab"><font color="Green" title="E103">A62</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>
<a NAME="E82:43"/>
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c8">w2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:43_5"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c8">w2</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="E2:43_5"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c3">u</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:43"><span class="lab"><font color="Green" title="E66">A23</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:43_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:43"><span class="lab"><font color="Green" title="E67">A24</font></span></a>, <a class="ref" href="anproj_1.html#T10" title="ANPROJ_1:th.10">ANPROJ_1:10</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="E83:43"/><span class="kw">then </span>
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:43"><span class="lab"><font color="Green" title="E74">A31</font></span></a>, <a class="txt" href="#E38:43"><span class="lab"><font color="Green" title="E75">A32</font></span></a>, <a class="txt" href="anproj_2.html#E30"><span class="lab"><font color="Green" title="E30">Lm17</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c30">A2</font>, <font color="Maroon" title="c31">B2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E85:43"/><span class="lab"><font color="Green" title="E103">A64</font></span>: 
<font color="Maroon" title="c10">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">A2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c31">B2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:43"><span class="lab"><font color="Green" title="E56">A13</font></span></a>, <a class="txt" href="#E55:43"><span class="lab"><font color="Green" title="E87">A44</font></span></a>, <a class="txt" href="#E57:43"><span class="lab"><font color="Green" title="E89">A46</font></span></a>, <a class="ref" href="anproj_1.html#T11" title="ANPROJ_1:th.11">ANPROJ_1:11</a></span>;<br/>
<a NAME="E86:43"/>
<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c10">v1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:43"><span class="lab"><font color="Green" title="E53">A10</font></span></a>, <a class="ref" href="anproj_1.html#T10" title="ANPROJ_1:th.10">ANPROJ_1:10</a></span>;<br/>
<a NAME="E87:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E104">A65</font></span>: 
<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>,<font color="Maroon" title="c10">v1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E62:43"><span class="lab"><font color="Green" title="E94">A51</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E88:43"/>
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c5">w</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:43"><span class="lab"><font color="Green" title="E67">A24</font></span></a>, <a class="txt" href="#E21:43"><span class="lab"><font color="Green" title="E64">A21</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E89:43"/><span class="kw">then </span>
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:43"><span class="lab"><font color="Green" title="E70">A27</font></span></a>, <a class="txt" href="#E31:43"><span class="lab"><font color="Green" title="E71">A28</font></span></a>, <a class="txt" href="anproj_2.html#E30"><span class="lab"><font color="Green" title="E30">Lm17</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c32">A29</font>, <font color="Maroon" title="c33">B29</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E91:43"/><span class="lab"><font color="Green" title="E105">A66</font></span>: 
<font color="Maroon" title="c10">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c32">A29</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c33">B29</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:43"><span class="lab"><font color="Green" title="E62">A19</font></span></a>, <a class="txt" href="#E54:43"><span class="lab"><font color="Green" title="E86">A43</font></span></a>, <a class="txt" href="#E87:43"><span class="lab"><font color="Green" title="E104">A65</font></span></a>, <a class="ref" href="anproj_1.html#T11" title="ANPROJ_1:th.11">ANPROJ_1:11</a></span>;<br/>
<a NAME="E92:43"/><span class="lab"><font color="Green" title="E106">A67</font></span>: 
<font color="Maroon" title="c10">v1</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="c31">B2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c30">A2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c31">B2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E85:43"><span class="lab"><font color="Green" title="E103">A64</font></span></a>, <a class="txt" href="anproj_2.html#E31"><span class="lab"><font color="Green" title="E31">Lm18</font></span></a></span>;<br/>
<a NAME="E93:43"/><span class="lab"><font color="Green" title="E107">A68</font></span>: 
<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>,<font color="Maroon" title="c11">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:43"><span class="lab"><font color="Green" title="E51">A8</font></span></a>, <a class="txt" href="#E58:43"><span class="lab"><font color="Green" title="E90">A47</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E94:43"/>
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c4">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:43"><span class="lab"><font color="Green" title="E67">A24</font></span></a>, <a class="txt" href="#E39:43"><span class="lab"><font color="Green" title="E76">A33</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E95:43"/><span class="kw">then </span>
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:43"><span class="lab"><font color="Green" title="E82">A39</font></span></a>, <a class="txt" href="#E51:43"><span class="lab"><font color="Green" title="E83">A40</font></span></a>, <a class="txt" href="anproj_2.html#E30"><span class="lab"><font color="Green" title="E30">Lm17</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c34">A39</font>, <font color="Maroon" title="c35">B39</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E97:43"/><span class="lab"><font color="Green" title="E108">A69</font></span>: 
<font color="Maroon" title="c11">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c34">A39</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c35">B39</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:43"><span class="lab"><font color="Green" title="E62">A19</font></span></a>, <a class="txt" href="#E93:43"><span class="lab"><font color="Green" title="E107">A68</font></span></a>, <a class="txt" href="#E53:43"><span class="lab"><font color="Green" title="E85">A42</font></span></a>, <a class="ref" href="anproj_1.html#T11" title="ANPROJ_1:th.11">ANPROJ_1:11</a></span>;<br/>
<a NAME="E98:43"/><span class="lab"><font color="Green" title="E109">A70</font></span>: 
<font color="Maroon" title="c11">w1</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="c25">B3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">A3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c25">B3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E67:43"><span class="lab"><font color="Green" title="E96">A53</font></span></a>, <a class="txt" href="anproj_2.html#E31"><span class="lab"><font color="Green" title="E31">Lm18</font></span></a></span>;<br/>
<a NAME="E99:43"/>
<font color="Maroon" title="c10">v1</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="c33">B29</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c33">B29</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a3</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c32">A29</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E91:43"><span class="lab"><font color="Green" title="E105">A66</font></span></a>, <a class="txt" href="anproj_2.html#E32"><span class="lab"><font color="Green" title="E32">Lm19</font></span></a></span>;<br/>
<a NAME="E100:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E110">A71</font></span>: 
( <font color="Maroon" title="c31">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c33">B29</font> &amp; <font color="Maroon" title="c30">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c33">B29</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a3</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:43"><span class="lab"><font color="Green" title="E67">A24</font></span></a>, <a class="txt" href="#E92:43"><span class="lab"><font color="Green" title="E106">A67</font></span></a>, <a class="ref" href="anproj_1.html#T13" title="ANPROJ_1:th.13">ANPROJ_1:13</a></span>;<br/>
<a NAME="E101:43"/>
<font color="Maroon" title="c11">w1</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="c35">B39</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c35">B39</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">a2</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c34">A39</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E97:43"><span class="lab"><font color="Green" title="E108">A69</font></span></a>, <a class="txt" href="anproj_2.html#E32"><span class="lab"><font color="Green" title="E32">Lm19</font></span></a></span>;<br/>
<a NAME="E102:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E111">A72</font></span>: 
( <font color="Maroon" title="c25">B3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c35">B39</font> &amp; <font color="Maroon" title="c24">A3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c35">B39</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">a2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:43"><span class="lab"><font color="Green" title="E67">A24</font></span></a>, <a class="txt" href="#E98:43"><span class="lab"><font color="Green" title="E109">A70</font></span></a>, <a class="ref" href="anproj_1.html#T13" title="ANPROJ_1:th.13">ANPROJ_1:13</a></span>;<br/>
<a NAME="E103:43"/><span class="lab"><font color="Green" title="E112">A73</font></span>: 
<font color="Maroon" title="c9">u1</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"><font color="Maroon" title="c28">A19</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c29">B19</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c28">A19</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a3</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c29">B19</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E77:43"><span class="lab"><font color="Green" title="E98">A57</font></span></a>, <a class="txt" href="anproj_2.html#E35"><span class="lab"><font color="Green" title="E35">Lm22</font></span></a></span>;<br/>
<a NAME="E104:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E113">A74</font></span>: 
<font color="Maroon" title="c27">B1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">B19</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:43"><span class="lab"><font color="Green" title="E67">A24</font></span></a>, <a class="txt" href="#E78:43"><span class="lab"><font color="Green" title="E99">A58</font></span></a>, <a class="ref" href="anproj_1.html#T13" title="ANPROJ_1:th.13">ANPROJ_1:13</a></span>;<br/>
<a NAME="E105:43"/>
( <font color="Maroon" title="c26">A1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c27">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">A19</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c29">B19</font> &amp; <font color="Maroon" title="c26">A1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">A19</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a3</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:43"><span class="lab"><font color="Green" title="E67">A24</font></span></a>, <a class="txt" href="#E78:43"><span class="lab"><font color="Green" title="E99">A58</font></span></a>, <a class="txt" href="#E103:43"><span class="lab"><font color="Green" title="E112">A73</font></span></a>, <a class="ref" href="anproj_1.html#T13" title="ANPROJ_1:th.13">ANPROJ_1:13</a></span>;<br/>
<a NAME="E106:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E114">A75</font></span>: 
<font color="Maroon" title="c26">A1</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"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span></span>)</span> <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> <font color="Maroon" title="c27">B1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:43"><span class="lab"><font color="Green" title="E79">A36</font></span></a>, <a class="txt" href="#E81:43"><span class="lab"><font color="Green" title="E102">A61</font></span></a>, <a class="txt" href="#E104:43"><span class="lab"><font color="Green" title="E113">A74</font></span></a>, <a class="txt" href="anproj_2.html#E37"><span class="lab"><font color="Green" title="E37">Lm24</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c36">v19</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c37">C2</font> = <font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c38">C3</font> =  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c39">u19</font> = <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">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a3</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c16">c2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <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"><font color="Maroon" title="c16">c2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c18">a2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c40">w19</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>;<br/>
<a NAME="E107:43"/><span class="lab"><font color="Green" title="E115">A76</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">a3</font></span>)</span>
 
;<br/>
<a NAME="E108:43"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a3</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">a2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a3</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c14">c3</font></span>)</span> )
 
;<br/>
<a NAME="E109:43"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a3</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c16">c2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c18">a2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="txt" href="#E107:43"><span class="lab"><font color="Green" title="E115">A76</font></span></a>, <a class="txt" href="anproj_2.html#E41"><span class="lab"><font color="Green" title="E41">Lm28</font></span></a></span>;<br/>
<a NAME="E110:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E116">A77</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">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a3</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c16">c2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <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"><font color="Maroon" title="c16">c2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c18">a2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_1.html#D3" title="ANPROJ_1:def.3">ANPROJ_1:def 3</a></span>;<br/>
<a NAME="E111:43"/><span class="lab"><font color="Green" title="E117">A78</font></span>: 
not <font color="Maroon" title="c10">v1</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:43"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E112:43"/><span class="lab"><font color="Green" title="E118">A79</font></span>: 
<font color="Maroon" title="c31">B2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:43_6"/>
not <font color="Maroon" title="c31">B2</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"> contradiction</span><br/>

<span class="kw">then </span><font color="Maroon" title="c10">v1</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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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> <span class="p2">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E85:43"><span class="lab"><font color="Green" title="E103">A64</font></span></a>, <a class="txt" href="#E100:43"><span class="lab"><font color="Green" title="E110">A71</font></span></a>, <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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>
<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/>
<span class="kw">hence </span><a NAME="E3:43_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E111:43"><span class="lab"><font color="Green" title="E117">A78</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>
<a NAME="E113:43"/>
<font color="Maroon" title="c10">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c31">B2</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="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E92:43"><span class="lab"><font color="Green" title="E106">A67</font></span></a>, <a class="txt" href="#E100:43"><span class="lab"><font color="Green" title="E110">A71</font></span></a>, <a class="txt" href="anproj_2.html#E42"><span class="lab"><font color="Green" title="E42">Lm29</font></span></a></span>;<br/>
<a NAME="E114:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E119">A80</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>,<font color="Maroon" title="c10">v1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E112:43"><span class="lab"><font color="Green" title="E118">A79</font></span></a>, <a class="txt" href="anproj_2.html#E29"><span class="lab"><font color="Green" title="E29">Lm16</font></span></a></span>;<br/>
<a NAME="E115:43"/><span class="lab"><font color="Green" title="E120">A81</font></span>: 
not <font color="Maroon" title="c11">w1</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:43"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E116:43"/><span class="lab"><font color="Green" title="E121">A82</font></span>: 
<font color="Maroon" title="c25">B3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_7"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:43_7"/>
not <font color="Maroon" title="c25">B3</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"> contradiction</span><br/>

<span class="kw">then </span><font color="Maroon" title="c11">w1</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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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> <span class="p2">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E67:43"><span class="lab"><font color="Green" title="E96">A53</font></span></a>, <a class="txt" href="#E102:43"><span class="lab"><font color="Green" title="E111">A72</font></span></a>, <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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>
<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/>
<span class="kw">hence </span><a NAME="E3:43_7"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E115:43"><span class="lab"><font color="Green" title="E120">A81</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>
<a NAME="E117:43"/>
<font color="Maroon" title="c11">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">B3</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="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E98:43"><span class="lab"><font color="Green" title="E109">A70</font></span></a>, <a class="txt" href="#E102:43"><span class="lab"><font color="Green" title="E111">A72</font></span></a>, <a class="txt" href="anproj_2.html#E42"><span class="lab"><font color="Green" title="E42">Lm29</font></span></a></span>;<br/>
<a NAME="E118:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E122">A83</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>,<font color="Maroon" title="c11">w1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E116:43"><span class="lab"><font color="Green" title="E121">A82</font></span></a>, <a class="txt" href="anproj_2.html#E29"><span class="lab"><font color="Green" title="E29">Lm16</font></span></a></span>;<br/>
<a NAME="E119:43"/><span class="lab"><font color="Green" title="E123">A84</font></span>: 
not <font color="Maroon" title="c9">u1</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:43"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E120:43"/><span class="lab"><font color="Green" title="E124">A85</font></span>: 
<font color="Maroon" title="c27">B1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_8"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:43_8"/>
not <font color="Maroon" title="c27">B1</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"> contradiction</span><br/>

<span class="kw">then </span><font color="Maroon" title="c9">u1</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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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> <span class="p2">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E72:43"><span class="lab"><font color="Green" title="E97">A55</font></span></a>, <a class="txt" href="#E106:43"><span class="lab"><font color="Green" title="E114">A75</font></span></a>, <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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>
<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/>
<span class="kw">hence </span><a NAME="E3:43_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E119:43"><span class="lab"><font color="Green" title="E123">A84</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>
<a NAME="E121:43"/>
<font color="Maroon" title="c9">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c27">B1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a3</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c16">c2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c16">c2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c18">a2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:43"><span class="lab"><font color="Green" title="E79">A36</font></span></a>, <a class="txt" href="#E81:43"><span class="lab"><font color="Green" title="E102">A61</font></span></a>, <a class="txt" href="#E78:43"><span class="lab"><font color="Green" title="E99">A58</font></span></a>, <a class="txt" href="#E106:43"><span class="lab"><font color="Green" title="E114">A75</font></span></a>, <a class="txt" href="anproj_2.html#E39"><span class="lab"><font color="Green" title="E39">Lm26</font></span></a></span>;<br/>
<a NAME="E122:43"/><span class="kw">then </span>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</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">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c18">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a3</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c14">c3</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c16">c2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span> <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"><font color="Maroon" title="c16">c2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c3</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c18">a2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>,<font color="Maroon" title="c9">u1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:43"><span class="lab"><font color="Green" title="E79">A36</font></span></a>, <a class="txt" href="#E81:43"><span class="lab"><font color="Green" title="E102">A61</font></span></a>, <a class="txt" href="#E120:43"><span class="lab"><font color="Green" title="E124">A85</font></span></a>, <a class="txt" href="anproj_2.html#E29"><span class="lab"><font color="Green" title="E29">Lm16</font></span></a>, <a class="txt" href="anproj_2.html#E38"><span class="lab"><font color="Green" title="E38">Lm25</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E123:43"/>
<font color="Maroon" title="c9">u1</font>,<font color="Maroon" title="c10">v1</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E118:43"><span class="lab"><font color="Green" title="E122">A83</font></span></a>, <a class="txt" href="#E114:43"><span class="lab"><font color="Green" title="E119">A80</font></span></a>, <a class="txt" href="#E110:43"><span class="lab"><font color="Green" title="E116">A77</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</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>
