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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/><b>let </b><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>;<br/>





















<b>assume </b><b>that </b><br/><a NAME="E1:43"/><i><font color="Green" title="E44">A1</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</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>  )
 <b>and </b><br/><a NAME="E2:43"/><i><font color="Green" title="E45">A2</font></i>: 
<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> 
 <b>and </b><br/><a NAME="E3:43"/><i><font color="Green" title="E46">A3</font></i>: 
<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> 
 <b>and </b><br/><a NAME="E4:43"/><i><font color="Green" title="E47">A4</font></i>: 
( <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>  )
 ;<br/>

<a NAME="E5:43"/><i><font color="Green" title="E48">A5</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c3">u</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c4">v</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c5">w</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c6">u2</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c7">v2</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c8">w2</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c9">u1</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c10">v1</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c11">w1</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E1:43"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></i>;<br/>
<a NAME="E6:43"/><i><font color="Green" title="E49">A6</font></i>: 
( 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>  &amp; <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>  &amp; <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>  &amp; <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>  &amp; <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>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E2:43"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="anproj_2.html#D4" target="_self" title="ANPROJ_2:def.4">Def4</a></i>;<br/>
<a NAME="E7:43"/><i><font color="Green" title="E50">A7</font></i>: 
( 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> &amp; 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="c2">o</font>,<font color="Maroon" title="c7">v2</font> &amp; 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="c3">u</font>,<font color="Maroon" title="c4">v</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> &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="c7">v2</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> &amp; 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> &amp; 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> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E3:43"><i><font color="Green" title="E46">A3</font></i></a>, <a class="ref" href="anproj_2.html#D5" target="_self" title="ANPROJ_2:def.5">Def5</a></i>;<br/>
<a NAME="E8:43"/><i><font color="Green" title="E51">A8</font></i>: 
( 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> &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="c6">u2</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="c2">o</font> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="anproj_1.html#T17" title="ANPROJ_1:th.17">ANPROJ_1:17</a></i>;<br/>
<a NAME="E9:43"/><i><font color="Green" title="E52">A9</font></i>: 
( <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>  &amp; <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>  &amp; <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>  &amp; <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>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green" title="E48">A5</font></i></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c12">a2</font>, <font color="Maroon" title="c13">b2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E11:43"/><i><font color="Green" title="E53">A10</font></i>: 
( <font color="Maroon" title="c13">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="c12">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> &amp; <font color="Maroon" title="c12">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>  &amp; <font color="Maroon" title="c13">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>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="txt" href="anproj_2.html#E7:43"><i><font color="Green" title="E50">A7</font></i></a>, <a class="txt" href="anproj_2.html#E8:43"><i><font color="Green" title="E51">A8</font></i></a>, <a class="ref" href="anproj_2.html#T6" target="_self" title="ANPROJ_2:th.6">Th6</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c14">a3</font>, <font color="Maroon" title="c15">b3</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E13:43"/><i><font color="Green" title="E54">A11</font></i>: 
( <font color="Maroon" title="c15">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="c14">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> &amp; <font color="Maroon" title="c14">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>  &amp; <font color="Maroon" title="c15">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>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="txt" href="anproj_2.html#E7:43"><i><font color="Green" title="E50">A7</font></i></a>, <a class="txt" href="anproj_2.html#E8:43"><i><font color="Green" title="E51">A8</font></i></a>, <a class="txt" href="anproj_2.html#E9:43"><i><font color="Green" title="E52">A9</font></i></a>, <a class="ref" href="anproj_2.html#T6" target="_self" title="ANPROJ_2:th.6">Th6</a></i>;<br/>
<b>consider </b><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><b> such that </b><br/><a NAME="E15:43"/><i><font color="Green" title="E55">A12</font></i>: 
( <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> &amp; <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>  &amp; <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>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="txt" href="anproj_2.html#E7:43"><i><font color="Green" title="E50">A7</font></i></a>, <a class="txt" href="anproj_2.html#E8:43"><i><font color="Green" title="E51">A8</font></i></a>, <a class="txt" href="anproj_2.html#E9:43"><i><font color="Green" title="E52">A9</font></i></a>, <a class="ref" href="anproj_2.html#T6" target="_self" title="ANPROJ_2:th.6">Th6</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c18">c3</font>, <font color="Maroon" title="c19">d3</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E17:43"/><i><font color="Green" title="E56">A13</font></i>: 
( <font color="Maroon" title="c19">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="c18">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span> &amp; <font color="Maroon" title="c18">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>  &amp; <font color="Maroon" title="c19">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>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="txt" href="anproj_2.html#E7:43"><i><font color="Green" title="E50">A7</font></i></a>, <a class="txt" href="anproj_2.html#E8:43"><i><font color="Green" title="E51">A8</font></i></a>, <a class="txt" href="anproj_2.html#E9:43"><i><font color="Green" title="E52">A9</font></i></a>, <a class="ref" href="anproj_2.html#T6" target="_self" title="ANPROJ_2:th.6">Th6</a></i>;<br/>
<b>set </b><font color="Maroon" title="c20">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">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c21">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="c14">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c22">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>;<br/>
<b>set </b><font color="Maroon" title="c23">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="c18">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="E18:43"/><i><font color="Green" title="E57">A14</font></i>: 
(  <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">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> &amp;  <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="c14">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> &amp;  <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> &amp;  <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="c18">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E11:43"><i><font color="Green" title="E53">A10</font></i></a>, <a class="txt" href="anproj_2.html#E13:43"><i><font color="Green" title="E54">A11</font></i></a>, <a class="txt" href="anproj_2.html#E15:43"><i><font color="Green" title="E55">A12</font></i></a>, <a class="txt" href="anproj_2.html#E17:43"><i><font color="Green" title="E56">A13</font></i></a>, <a class="txt" href="anproj_2.html#E29"><i><font color="Green" title="E29">Lm16</font></i></a></i>;<br/>
<a NAME="E19:43"/><i><font color="Green" title="E58">A15</font></i>: 
( 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">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">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="c18">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_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_1"/><i><font color="Green" title="E59">A16</font></i>: 
(  <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">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">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="c18">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span> )
 ;<br/>

<div><i><font color="Green" title="E60">A17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:43_1_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="c12">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">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>
 ;<br/><a NAME="E2:43_1_1"/><b>then </b>
 <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="c14">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>
 <b>by </b><i><a class="txt" href="anproj_2.html#E18:43"><i><font color="Green" title="E57">A14</font></i></a>, <a class="ref" href="anproj_1.html#T6" title="ANPROJ_1:th.6">ANPROJ_1:6</a></i>;<br/><b>hence </b><a NAME="E3:43_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E7:43"><i><font color="Green" title="E50">A7</font></i></a>, <a class="txt" href="anproj_2.html#E18:43"><i><font color="Green" title="E57">A14</font></i></a>, <a class="ref" href="anproj_1.html#T6" title="ANPROJ_1:th.6">ANPROJ_1:6</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:43_1_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="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="c18">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="E2:43_1_2"/><b>then </b>
 <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="c18">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 <b>by </b><i><a class="txt" href="anproj_2.html#E18:43"><i><font color="Green" title="E57">A14</font></i></a>, <a class="ref" href="anproj_1.html#T6" title="ANPROJ_1:th.6">ANPROJ_1:6</a></i>;<br/><b>hence </b><a NAME="E3:43_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E7:43"><i><font color="Green" title="E50">A7</font></i></a>, <a class="txt" href="anproj_2.html#E18:43"><i><font color="Green" title="E57">A14</font></i></a>, <a class="ref" href="anproj_1.html#T6" title="ANPROJ_1:th.6">ANPROJ_1:6</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:43_1"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:43_1"><i><font color="Green" title="E59">A16</font></i></a>, <a class="txt" href="anproj_2.html#E2:43_1"><i><font color="Green" title="E60">A17</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E20:43"/><i><font color="Green" title="E59">A18</font></i>: 
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_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_2"/>
 <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>
 ;<br/>

<a NAME="E2:43_2"/><b>then </b>
<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> 
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>
<b>hence </b><a NAME="E3:43_2"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="anproj_1.html#T10" title="ANPROJ_1:th.10">ANPROJ_1:10</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E21:43"/><i><font color="Green" title="E60">A19</font></i>: 
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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>
<a NAME="E22:43"/><i><font color="Green" title="E61">A20</font></i>: 
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_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_3"/>
 <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>
 ;<br/>

<a NAME="E2:43_3"/><b>then </b>
<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> 
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>
<b>hence </b><a NAME="E3:43_3"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="anproj_1.html#T10" title="ANPROJ_1:th.10">ANPROJ_1:10</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E23:43"/><i><font color="Green" title="E62">A21</font></i>: 
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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>
<a NAME="E24:43"/>
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_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_4"/>
<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> 
 ;<br/>

<a NAME="E2:43_4"/><b>then </b><i><font color="Green" title="E63">A22</font></i>: 
<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> 
 
<b>by </b><i><a class="ref" href="anproj_1.html#T10" title="ANPROJ_1:th.10">ANPROJ_1:10</a></i>;<br/>
<a NAME="E3:43_4"/><i><font color="Green" title="E64">A23</font></i>: 
<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> 
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="anproj_1.html#T10" title="ANPROJ_1:th.10">ANPROJ_1:10</a></i>;<br/>
<a NAME="E4:43_4"/>
<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> 
 
<b>by </b><i><a class="ref" href="anproj_1.html#T16" title="ANPROJ_1:th.16">ANPROJ_1:16</a></i>;<br/>
<b>hence </b><a NAME="E5:43_4"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green" title="E48">A5</font></i></a>, <a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="txt" href="anproj_2.html#E7:43"><i><font color="Green" title="E50">A7</font></i></a>, <a class="txt" href="anproj_2.html#E2:43_4"><i><font color="Green" title="E63">A22</font></i></a>, <a class="txt" href="anproj_2.html#E3:43_4"><i><font color="Green" title="E64">A23</font></i></a>, <a class="ref" href="anproj_1.html#T19" title="ANPROJ_1:th.19">ANPROJ_1:19</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E25:43"/><b>then </b><i><font color="Green" title="E63">A24</font></i>: 
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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>
<a NAME="E26:43"/>
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_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_5"/>
<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> 
 ;<br/>

<a NAME="E2:43_5"/><b>then </b><i><font color="Green" title="E64">A25</font></i>: 
<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> 
 
<b>by </b><i><a class="ref" href="anproj_1.html#T10" title="ANPROJ_1:th.10">ANPROJ_1:10</a></i>;<br/>
<a NAME="E3:43_5"/><i><font color="Green" title="E65">A26</font></i>: 
<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> 
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="anproj_1.html#T10" title="ANPROJ_1:th.10">ANPROJ_1:10</a></i>;<br/>
<a NAME="E4:43_5"/>
<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> 
 
<b>by </b><i><a class="ref" href="anproj_1.html#T16" title="ANPROJ_1:th.16">ANPROJ_1:16</a></i>;<br/>
<b>hence </b><a NAME="E5:43_5"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green" title="E48">A5</font></i></a>, <a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="txt" href="anproj_2.html#E7:43"><i><font color="Green" title="E50">A7</font></i></a>, <a class="txt" href="anproj_2.html#E2:43_5"><i><font color="Green" title="E64">A25</font></i></a>, <a class="txt" href="anproj_2.html#E3:43_5"><i><font color="Green" title="E65">A26</font></i></a>, <a class="ref" href="anproj_1.html#T19" title="ANPROJ_1:th.19">ANPROJ_1:19</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E27:43"/><b>then </b><i><font color="Green" title="E64">A27</font></i>: 
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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>
<a NAME="E28:43"/><i><font color="Green" title="E65">A28</font></i>: 
( <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>  &amp; <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">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>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E4:43"><i><font color="Green" title="E47">A4</font></i></a>, <a class="txt" href="anproj_2.html#E18:43"><i><font color="Green" title="E57">A14</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>
<a NAME="E29:43"/><i><font color="Green" title="E66">A29</font></i>: 
<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> 
 
<b>by </b><i><a class="txt" href="anproj_2.html#E4:43"><i><font color="Green" title="E47">A4</font></i></a>, <a class="ref" href="anproj_1.html#T10" title="ANPROJ_1:th.10">ANPROJ_1:10</a></i>;<br/>
<a NAME="E30:43"/><i><font color="Green" title="E67">A30</font></i>: 
( <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> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <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">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="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <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">c3</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#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <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">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="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green" title="E48">A5</font></i></a>, <a class="txt" href="anproj_2.html#E11:43"><i><font color="Green" title="E53">A10</font></i></a>, <a class="txt" href="anproj_2.html#E13:43"><i><font color="Green" title="E54">A11</font></i></a>, <a class="txt" href="anproj_2.html#E15:43"><i><font color="Green" title="E55">A12</font></i></a>, <a class="txt" href="anproj_2.html#E17:43"><i><font color="Green" title="E56">A13</font></i></a>, <a class="txt" href="anproj_2.html#E33"><i><font color="Green" title="E33">Lm20</font></i></a></i>;<br/>
<a NAME="E31:43"/><i><font color="Green" title="E68">A31</font></i>: 
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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E15:43"><i><font color="Green" title="E55">A12</font></i></a>, <a class="txt" href="anproj_2.html#E20:43"><i><font color="Green" title="E59">A18</font></i></a>, <a class="txt" href="anproj_2.html#E30"><i><font color="Green" title="E30">Lm17</font></i></a></i>;<br/>
<a NAME="E32:43"/><i><font color="Green" title="E69">A32</font></i>: 
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">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E11:43"><i><font color="Green" title="E53">A10</font></i></a>, <a class="txt" href="anproj_2.html#E21:43"><i><font color="Green" title="E60">A19</font></i></a>, <a class="txt" href="anproj_2.html#E30"><i><font color="Green" title="E30">Lm17</font></i></a></i>;<br/>
<a NAME="E33:43"/><i><font color="Green" title="E70">A33</font></i>: 
<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="c18">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> 
 
<b>by </b><i><a class="txt" href="anproj_2.html#E4:43"><i><font color="Green" title="E47">A4</font></i></a>, <a class="txt" href="anproj_2.html#E18:43"><i><font color="Green" title="E57">A14</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>
<a NAME="E34:43"/><i><font color="Green" title="E71">A34</font></i>: 
<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="c14">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> 
 
<b>by </b><i><a class="txt" href="anproj_2.html#E18:43"><i><font color="Green" title="E57">A14</font></i></a>, <a class="txt" href="anproj_2.html#E29:43"><i><font color="Green" title="E66">A29</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>
<a NAME="E35:43"/><i><font color="Green" title="E72">A35</font></i>: 
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="c18">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E17:43"><i><font color="Green" title="E56">A13</font></i></a>, <a class="txt" href="anproj_2.html#E22:43"><i><font color="Green" title="E61">A20</font></i></a>, <a class="txt" href="anproj_2.html#E30"><i><font color="Green" title="E30">Lm17</font></i></a></i>;<br/>
<a NAME="E36:43"/><i><font color="Green" title="E73">A36</font></i>: 
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="c14">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E13:43"><i><font color="Green" title="E54">A11</font></i></a>, <a class="txt" href="anproj_2.html#E23:43"><i><font color="Green" title="E62">A21</font></i></a>, <a class="txt" href="anproj_2.html#E30"><i><font color="Green" title="E30">Lm17</font></i></a></i>;<br/>
<b>consider </b><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><b> such that </b><br/><a NAME="E38:43"/><i><font color="Green" title="E74">A37</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green" title="E48">A5</font></i></a>, <a class="txt" href="anproj_2.html#E28:43"><i><font color="Green" title="E65">A28</font></i></a>, <a class="txt" href="anproj_2.html#E30:43"><i><font color="Green" title="E67">A30</font></i></a>, <a class="txt" href="anproj_2.html#E31:43"><i><font color="Green" title="E68">A31</font></i></a>, <a class="ref" href="anproj_1.html#T11" title="ANPROJ_1:th.11">ANPROJ_1:11</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c26">A3'</font>, <font color="Maroon" title="c27">B3'</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E40:43"/><i><font color="Green" title="E75">A38</font></i>: 
<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="c26">A3'</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="c27">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="c12">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>
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green" title="E48">A5</font></i></a>, <a class="txt" href="anproj_2.html#E28:43"><i><font color="Green" title="E65">A28</font></i></a>, <a class="txt" href="anproj_2.html#E30:43"><i><font color="Green" title="E67">A30</font></i></a>, <a class="txt" href="anproj_2.html#E32:43"><i><font color="Green" title="E69">A32</font></i></a>, <a class="ref" href="anproj_1.html#T11" title="ANPROJ_1:th.11">ANPROJ_1:11</a></i>;<br/>
<a NAME="E41:43"/><i><font color="Green" title="E76">A39</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E38:43"><i><font color="Green" title="E74">A37</font></i></a>, <a class="txt" href="anproj_2.html#E31"><i><font color="Green" title="E31">Lm18</font></i></a></i>;<br/>
<a NAME="E42:43"/>
<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="c27">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"><span class="p3">(<span class="default"><font color="Maroon" title="c27">B3'</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">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="c26">A3'</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E40:43"><i><font color="Green" title="E75">A38</font></i></a>, <a class="txt" href="anproj_2.html#E32"><i><font color="Green" title="E32">Lm19</font></i></a></i>;<br/>
<a NAME="E43:43"/><b>then </b><i><font color="Green" title="E77">A40</font></i>: 
( <font color="Maroon" title="c25">B3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">B3'</font> &amp; <font color="Maroon" title="c24">A3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">B3'</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a2</font> &amp; <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">A3'</font> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="txt" href="anproj_2.html#E41:43"><i><font color="Green" title="E76">A39</font></i></a>, <a class="ref" href="anproj_1.html#T13" title="ANPROJ_1:th.13">ANPROJ_1:13</a></i>;<br/>
<b>set </b><font color="Maroon" title="c28">w1'</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">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="E44:43"/><i><font color="Green" title="E78">A41</font></i>: 
<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_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_6"/>
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> 
 ;<br/>

<b>then </b><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>
<b>by </b><i><a class="txt" href="anproj_2.html#E38:43"><i><font color="Green" title="E74">A37</font></i></a>, <a class="txt" href="anproj_2.html#E43:43"><i><font color="Green" title="E77">A40</font></i></a>, <a class="ref" href="rlvect_1.html#T23" title="RLVECT_1:th.23">RLVECT_1:23</a></i>
<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>
<b>by </b><i><a class="ref" href="rlvect_1.html#T23" title="RLVECT_1:th.23">RLVECT_1:23</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10" title="RLVECT_1:th.10">RLVECT_1:10</a></i>
;<br/>
<b>hence </b><a NAME="E3:43_6"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green" title="E48">A5</font></i></a>, <a class="ref" href="rlvect_1.html#D14" title="RLVECT_1:def.14">RLVECT_1:def 14</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E45:43"/>
<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="c12">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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E41:43"><i><font color="Green" title="E76">A39</font></i></a>, <a class="txt" href="anproj_2.html#E43:43"><i><font color="Green" title="E77">A40</font></i></a>, <a class="txt" href="anproj_2.html#E42"><i><font color="Green" title="E42">Lm29</font></i></a></i>;<br/>
<a NAME="E46:43"/><b>then </b><i><font color="Green" title="E79">A42</font></i>: 
 <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">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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E44:43"><i><font color="Green" title="E78">A41</font></i></a>, <a class="txt" href="anproj_2.html#E29"><i><font color="Green" title="E29">Lm16</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c29">A2</font>, <font color="Maroon" title="c30">B2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E48:43"/><i><font color="Green" title="E80">A43</font></i>: 
<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="c29">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="c30">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="c18">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>
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green" title="E48">A5</font></i></a>, <a class="txt" href="anproj_2.html#E30:43"><i><font color="Green" title="E67">A30</font></i></a>, <a class="txt" href="anproj_2.html#E33:43"><i><font color="Green" title="E70">A33</font></i></a>, <a class="txt" href="anproj_2.html#E35:43"><i><font color="Green" title="E72">A35</font></i></a>, <a class="ref" href="anproj_1.html#T11" title="ANPROJ_1:th.11">ANPROJ_1:11</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c31">A2'</font>, <font color="Maroon" title="c32">B2'</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E50:43"/><i><font color="Green" title="E81">A44</font></i>: 
<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="c31">A2'</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="c32">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">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>
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green" title="E48">A5</font></i></a>, <a class="txt" href="anproj_2.html#E30:43"><i><font color="Green" title="E67">A30</font></i></a>, <a class="txt" href="anproj_2.html#E34:43"><i><font color="Green" title="E71">A34</font></i></a>, <a class="txt" href="anproj_2.html#E36:43"><i><font color="Green" title="E73">A36</font></i></a>, <a class="ref" href="anproj_1.html#T11" title="ANPROJ_1:th.11">ANPROJ_1:11</a></i>;<br/>
<a NAME="E51:43"/><i><font color="Green" title="E82">A45</font></i>: 
<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="c30">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="c29">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="c30">B2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E48:43"><i><font color="Green" title="E80">A43</font></i></a>, <a class="txt" href="anproj_2.html#E31"><i><font color="Green" title="E31">Lm18</font></i></a></i>;<br/>
<a NAME="E52:43"/>
<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="c32">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"><span class="p3">(<span class="default"><font color="Maroon" title="c32">B2'</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">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="c31">A2'</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E50:43"><i><font color="Green" title="E81">A44</font></i></a>, <a class="txt" href="anproj_2.html#E32"><i><font color="Green" title="E32">Lm19</font></i></a></i>;<br/>
<a NAME="E53:43"/><b>then </b><i><font color="Green" title="E83">A46</font></i>: 
( <font color="Maroon" title="c30">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c32">B2'</font> &amp; <font color="Maroon" title="c29">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c32">B2'</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">a3</font> &amp; <font color="Maroon" title="c30">B2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">c3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c31">A2'</font> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="txt" href="anproj_2.html#E51:43"><i><font color="Green" title="E82">A45</font></i></a>, <a class="ref" href="anproj_1.html#T13" title="ANPROJ_1:th.13">ANPROJ_1:13</a></i>;<br/>
<b>set </b><font color="Maroon" title="c33">v1'</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="c14">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="c18">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="E54:43"/><i><font color="Green" title="E84">A47</font></i>: 
<font color="Maroon" title="c30">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_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_7"/>
not <font color="Maroon" title="c30">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> 
 ;<br/>

<b>then </b><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="c18">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>
<b>by </b><i><a class="txt" href="anproj_2.html#E48:43"><i><font color="Green" title="E80">A43</font></i></a>, <a class="txt" href="anproj_2.html#E53:43"><i><font color="Green" title="E83">A46</font></i></a>, <a class="ref" href="rlvect_1.html#T23" title="RLVECT_1:th.23">RLVECT_1:23</a></i>
<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>
<b>by </b><i><a class="ref" href="rlvect_1.html#T23" title="RLVECT_1:th.23">RLVECT_1:23</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10" title="RLVECT_1:th.10">RLVECT_1:10</a></i>
;<br/>
<b>hence </b><a NAME="E3:43_7"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green" title="E48">A5</font></i></a>, <a class="ref" href="rlvect_1.html#D14" title="RLVECT_1:def.14">RLVECT_1:def 14</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E55:43"/>
<font color="Maroon" title="c10">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">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="c14">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="c18">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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E51:43"><i><font color="Green" title="E82">A45</font></i></a>, <a class="txt" href="anproj_2.html#E53:43"><i><font color="Green" title="E83">A46</font></i></a>, <a class="txt" href="anproj_2.html#E42"><i><font color="Green" title="E42">Lm29</font></i></a></i>;<br/>
<a NAME="E56:43"/><b>then </b><i><font color="Green" title="E85">A48</font></i>: 
 <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="c14">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="c18">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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E54:43"><i><font color="Green" title="E84">A47</font></i></a>, <a class="txt" href="anproj_2.html#E29"><i><font color="Green" title="E29">Lm16</font></i></a></i>;<br/>
<a NAME="E57:43"/><i><font color="Green" title="E86">A49</font></i>: 
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">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="c18">c3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E11:43"><i><font color="Green" title="E53">A10</font></i></a>, <a class="txt" href="anproj_2.html#E17:43"><i><font color="Green" title="E56">A13</font></i></a>, <a class="txt" href="anproj_2.html#E25:43"><i><font color="Green" title="E63">A24</font></i></a>, <a class="txt" href="anproj_2.html#E34"><i><font color="Green" title="E34">Lm21</font></i></a></i>;<br/>
<a NAME="E58:43"/><i><font color="Green" title="E87">A50</font></i>: 
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="c14">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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E13:43"><i><font color="Green" title="E54">A11</font></i></a>, <a class="txt" href="anproj_2.html#E15:43"><i><font color="Green" title="E55">A12</font></i></a>, <a class="txt" href="anproj_2.html#E27:43"><i><font color="Green" title="E64">A27</font></i></a>, <a class="txt" href="anproj_2.html#E34"><i><font color="Green" title="E34">Lm21</font></i></a></i>;<br/>
<a NAME="E59:43"/><i><font color="Green" title="E88">A51</font></i>: 
( <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">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="c18">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>  &amp; <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">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>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E4:43"><i><font color="Green" title="E47">A4</font></i></a>, <a class="txt" href="anproj_2.html#E18:43"><i><font color="Green" title="E57">A14</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c34">A1</font>, <font color="Maroon" title="c35">B1</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E61:43"/><i><font color="Green" title="E89">A52</font></i>: 
<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="c34">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="c12">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="c35">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="c18">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>
 <b>by </b><i><a class="txt" href="anproj_2.html#E30:43"><i><font color="Green" title="E67">A30</font></i></a>, <a class="txt" href="anproj_2.html#E57:43"><i><font color="Green" title="E86">A49</font></i></a>, <a class="ref" href="anproj_1.html#T11" title="ANPROJ_1:th.11">ANPROJ_1:11</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c36">A1'</font>, <font color="Maroon" title="c37">B1'</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E63:43"/><i><font color="Green" title="E90">A53</font></i>: 
<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="c36">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="c14">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="c37">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="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>
 <b>by </b><i><a class="txt" href="anproj_2.html#E30:43"><i><font color="Green" title="E67">A30</font></i></a>, <a class="txt" href="anproj_2.html#E58:43"><i><font color="Green" title="E87">A50</font></i></a>, <a class="txt" href="anproj_2.html#E59:43"><i><font color="Green" title="E88">A51</font></i></a>, <a class="ref" href="anproj_1.html#T11" title="ANPROJ_1:th.11">ANPROJ_1:11</a></i>;<br/>
<a NAME="E64:43"/><i><font color="Green" title="E91">A54</font></i>: 
<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="c34">A1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c35">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="c34">A1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">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="c35">B1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E61:43"><i><font color="Green" title="E89">A52</font></i></a>, <a class="txt" href="anproj_2.html#E35"><i><font color="Green" title="E35">Lm22</font></i></a></i>;<br/>
<a NAME="E65:43"/>
<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="c36">A1'</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c37">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="c36">A1'</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">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="c37">B1'</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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E63:43"><i><font color="Green" title="E90">A53</font></i></a>, <a class="txt" href="anproj_2.html#E35"><i><font color="Green" title="E35">Lm22</font></i></a></i>;<br/>
<a NAME="E66:43"/><b>then </b>
( <font color="Maroon" title="c34">A1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c35">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c36">A1'</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c37">B1'</font> &amp; <font color="Maroon" title="c34">A1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c36">A1'</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">a3</font> &amp; <font color="Maroon" title="c35">B1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">c3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">B1'</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green" title="E49">A6</font></i></a>, <a class="txt" href="anproj_2.html#E64:43"><i><font color="Green" title="E91">A54</font></i></a>, <a class="ref" href="anproj_1.html#T13" title="ANPROJ_1:th.13">ANPROJ_1:13</a></i>;<br/>
<a NAME="E67:43"/><b>then </b><i><font color="Green" title="E92">A55</font></i>: 
<font color="Maroon" title="c34">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="c14">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">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="c14">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="c14">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="c12">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="c35">B1</font>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E15:43"><i><font color="Green" title="E55">A12</font></i></a>, <a class="txt" href="anproj_2.html#E19:43"><i><font color="Green" title="E58">A15</font></i></a>, <a class="txt" href="anproj_2.html#E37"><i><font color="Green" title="E37">Lm24</font></i></a></i>;<br/>
<a NAME="E68:43"/><b>then </b><i><font color="Green" title="E93">A56</font></i>: 
<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="c35">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="c14">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="c12">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="c14">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">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="c12">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="c12">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">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="c18">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="c18">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="c14">a3</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E15:43"><i><font color="Green" title="E55">A12</font></i></a>, <a class="txt" href="anproj_2.html#E19:43"><i><font color="Green" title="E58">A15</font></i></a>, <a class="txt" href="anproj_2.html#E64:43"><i><font color="Green" title="E91">A54</font></i></a>, <a class="txt" href="anproj_2.html#E39"><i><font color="Green" title="E39">Lm26</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c38">u1'</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="c14">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">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="c12">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="c12">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">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="c18">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="c18">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="c14">a3</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">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/>
<a NAME="E69:43"/>
<font color="Maroon" title="c35">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"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_8"/>
not <font color="Maroon" title="c35">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> 
 ;<br/>

<b>then </b><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="c18">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>
<b>by </b><i><a class="txt" href="anproj_2.html#E61:43"><i><font color="Green" title="E89">A52</font></i></a>, <a class="txt" href="anproj_2.html#E67:43"><i><font color="Green" title="E92">A55</font></i></a>, <a class="ref" href="rlvect_1.html#T23" title="RLVECT_1:th.23">RLVECT_1:23</a></i>
<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>
<b>by </b><i><a class="ref" href="rlvect_1.html#T23" title="RLVECT_1:th.23">RLVECT_1:23</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10" title="RLVECT_1:th.10">RLVECT_1:10</a></i>
;<br/>
<b>hence </b><a NAME="E3:43_8"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green" title="E48">A5</font></i></a>, <a class="ref" href="rlvect_1.html#D14" title="RLVECT_1:def.14">RLVECT_1:def 14</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E70:43"/><b>then </b><i><font color="Green" title="E94">A57</font></i>: 
 <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="c14">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">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="c12">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="c12">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">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="c18">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="c18">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="c14">a3</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E15:43"><i><font color="Green" title="E55">A12</font></i></a>, <a class="txt" href="anproj_2.html#E19:43"><i><font color="Green" title="E58">A15</font></i></a>, <a class="txt" href="anproj_2.html#E68:43"><i><font color="Green" title="E93">A56</font></i></a>, <a class="txt" href="anproj_2.html#E29"><i><font color="Green" title="E29">Lm16</font></i></a>, <a class="txt" href="anproj_2.html#E38"><i><font color="Green" title="E38">Lm25</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c39">C2</font> = <font color="Maroon" title="c12">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">c2</font>;<br/>
<b>set </b><font color="Maroon" title="c40">C3</font> =  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">c3</font></span>)</span>;<br/>
<a NAME="E71:43"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c12">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="c14">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">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="c12">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="c14">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">c3</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">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">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="c14">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">c3</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">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="c18">c3</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">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="c18">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="c14">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">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="c18">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="c12">a2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c14">a3</font></span>)</span> )
 
;<br/>
<a NAME="E72:43"/><b>then </b>
<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="c14">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">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="c12">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="c12">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">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="c18">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="c18">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="c14">a3</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">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="c12">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="c14">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="c18">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="c14">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">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="c12">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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E41"><i><font color="Green" title="E41">Lm28</font></i></a></i>;<br/>
<a NAME="E73:43"/><b>then </b>
<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="c14">a3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c18">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="c12">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="c12">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">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="c18">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="c18">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="c14">a3</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">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="c14">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="c18">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="c12">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> 
 
<b>by </b><i><a class="ref" href="anproj_1.html#D3" title="ANPROJ_1:def.3">ANPROJ_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E74:43"/>
<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> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E46:43"><i><font color="Green" title="E79">A42</font></i></a>, <a class="txt" href="anproj_2.html#E56:43"><i><font color="Green" title="E85">A48</font></i></a>, <a class="txt" href="anproj_2.html#E70:43"><i><font color="Green" title="E94">A57</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>


</div>
