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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">u</font>, <font color="Olive" title="b3">v</font>, <font color="Olive" title="b4">w</font>, <font color="Olive" title="b5">u2</font>, <font color="Olive" title="b6">v2</font>, <font color="Olive" title="b7">w2</font>, <font color="Olive" title="b8">u1</font>, <font color="Olive" title="b9">v1</font>, <font color="Olive" title="b10">w1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font>  st  not <font color="Olive" title="b1">o</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  &amp; <font color="Olive" title="b2">u</font>,<font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">w</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a>  &amp; <font color="Olive" title="b5">u2</font>,<font color="Olive" title="b6">v2</font>,<font color="Olive" title="b7">w2</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a>  &amp; <font color="Olive" title="b8">u1</font>,<font color="Olive" title="b9">v1</font>,<font color="Olive" title="b10">w1</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">u</font>,<font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">w</font>,<font color="Olive" title="b5">u2</font>,<font color="Olive" title="b6">v2</font>,<font color="Olive" title="b7">w2</font> <a href="anproj_2.html#R3" title="ANPROJ_2:pred.3">are_perspective</a>  &amp;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">u2</font> &amp;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b6">v2</font> &amp;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b7">w2</font> &amp;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Olive" title="b2">u</font>,<font color="Olive" title="b5">u2</font> &amp;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Olive" title="b3">v</font>,<font color="Olive" title="b6">v2</font> &amp;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Olive" title="b4">w</font>,<font color="Olive" title="b7">w2</font> &amp;  not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">u</font>,<font color="Olive" title="b3">v</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp;  not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">u</font>,<font color="Olive" title="b4">w</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp;  not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">w</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Olive" title="b2">u</font>,<font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">w</font>,<font color="Olive" title="b8">u1</font>,<font color="Olive" title="b9">v1</font>,<font color="Olive" title="b10">w1</font> <a href="anproj_2.html#R2" title="ANPROJ_2:pred.2">lie_on_a_triangle</a>  &amp; <font color="Olive" title="b5">u2</font>,<font color="Olive" title="b6">v2</font>,<font color="Olive" title="b7">w2</font>,<font color="Olive" title="b8">u1</font>,<font color="Olive" title="b9">v1</font>,<font color="Olive" title="b10">w1</font> <a href="anproj_2.html#R2" title="ANPROJ_2:pred.2">lie_on_a_triangle</a>  holds <br/><font color="Olive" title="b8">u1</font>,<font color="Olive" title="b9">v1</font>,<font color="Olive" title="b10">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">u</font>, <font color="Maroon" title="c4">v</font>, <font color="Maroon" title="c5">w</font>, <font color="Maroon" title="c6">u2</font>, <font color="Maroon" title="c7">v2</font>, <font color="Maroon" title="c8">w2</font>, <font color="Maroon" title="c9">u1</font>, <font color="Maroon" title="c10">v1</font>, <font color="Maroon" title="c11">w1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">o</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  &amp; <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">w</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a>  &amp; <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c8">w2</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a>  &amp; <font color="Maroon" title="c9">u1</font>,<font color="Maroon" title="c10">v1</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c8">w2</font> <a href="anproj_2.html#R3" title="ANPROJ_2:pred.3">are_perspective</a>  &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="c6">u2</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="c6">u2</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="c7">v2</font> &amp;  not  <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="c8">w2</font> &amp;  not <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;  not <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;  not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">v</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="c3">u</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">w</font>,<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#R2" title="ANPROJ_2:pred.2">lie_on_a_triangle</a>  &amp; <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> <a href="anproj_2.html#R2" title="ANPROJ_2:pred.2">lie_on_a_triangle</a>  implies <font color="Maroon" title="c9">u1</font>,<font color="Maroon" title="c10">v1</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  )</span><br/>





















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:26"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
 not <font color="Maroon" title="c2">o</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E2:26"/><span class="lab"><font color="Green" title="E28">A2</font></span>: 
<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">w</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 <span class="kw">and </span><br/><a NAME="E3:26"/><span class="lab"><font color="Green" title="E29">A3</font></span>: 
<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c8">w2</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 <span class="kw">and </span><br/><a NAME="E4:26"/><span class="lab"><font color="Green" title="E30">A4</font></span>: 
<font color="Maroon" title="c9">u1</font>,<font color="Maroon" title="c10">v1</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 <span class="kw">and </span><br/><a NAME="E5:26"/><span class="lab"><font color="Green" title="E31">A5</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c8">w2</font> <a href="anproj_2.html#R3" title="ANPROJ_2:pred.3">are_perspective</a> 
 <span class="kw">and </span><br/><a NAME="E6:26"/><span class="lab"><font color="Green" title="E32">A6</font></span>: 
 not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">u2</font>
 <span class="kw">and </span><br/><a NAME="E7:26"/><span class="lab"><font color="Green" title="E33">A7</font></span>: 
 not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">v2</font>
 <span class="kw">and </span><br/><a NAME="E8:26"/><span class="lab"><font color="Green" title="E34">A8</font></span>: 
 not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">w2</font>
 <span class="kw">and </span><br/><a NAME="E9:26"/><span class="lab"><font color="Green" title="E35">A9</font></span>: 
 not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c6">u2</font>
 <span class="kw">and </span><br/><a NAME="E10:26"/><span class="lab"><font color="Green" title="E36">A10</font></span>: 
 not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c7">v2</font>
 <span class="kw">and </span><br/><a NAME="E11:26"/><span class="lab"><font color="Green" title="E37">A11</font></span>: 
 not  <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="c8">w2</font>
 <span class="kw">and </span><br/><a NAME="E12:26"/><span class="lab"><font color="Green" title="E38">A12</font></span>: 
 not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">and </span><br/><a NAME="E13:26"/><span class="lab"><font color="Green" title="E39">A13</font></span>: 
 not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c5">w</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">and </span><br/><a NAME="E14:26"/><span class="lab"><font color="Green" title="E40">A14</font></span>: 
 not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">w</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">and </span><br/><a NAME="E15:26"/><span class="lab"><font color="Green" title="E41">A15</font></span>: 
<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="c9">u1</font>,<font color="Maroon" title="c10">v1</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_2.html#R2" title="ANPROJ_2:pred.2">lie_on_a_triangle</a> 
 <span class="kw">and </span><br/><a NAME="E16:26"/><span class="lab"><font color="Green" title="E42">A16</font></span>: 
<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> <a href="anproj_2.html#R2" title="ANPROJ_2:pred.2">lie_on_a_triangle</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c9">u1</font>,<font color="Maroon" title="c10">v1</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> </span><br/>

<a NAME="E17:26"/><span class="lab"><font color="Green" title="E43">A17</font></span>: 
 not <font color="Maroon" title="c5">w</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E18:26"/><span class="lab"><font color="Green" title="E44">A18</font></span>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c8">w2</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp;  not  <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> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:26"><span class="lab"><font color="Green" title="E31">A5</font></span></a>, <a class="txt" href="#E13:26"><span class="lab"><font color="Green" title="E39">A13</font></span></a>, <a class="ref" href="anproj_2.html#D3" target="_self" title="ANPROJ_2:def.3">Def3</a>, <a class="ref" href="anproj_1.html#T11" title="ANPROJ_1:th.11">ANPROJ_1:11</a></span>;<br/>
<a NAME="E19:26"/><span class="lab"><font color="Green" title="E45">A19</font></span>: 
 not <font color="Maroon" title="c8">w2</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E20:26"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c8">w2</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E17:26"><span class="lab"><font color="Green" title="E43">A17</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">a3</font>, <font color="Maroon" title="c13">b3</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E22:26"/><span class="lab"><font color="Green" title="E46">A20</font></span>: 
<font color="Maroon" title="c13">b3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="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="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E23:26"/>
<font color="Maroon" title="c12">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E24:26"/><span class="lab"><font color="Green" title="E47">A21</font></span>: 
<font color="Maroon" title="c13">b3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:26"><span class="lab"><font color="Green" title="E34">A8</font></span></a>, <a class="txt" href="#E11:26"><span class="lab"><font color="Green" title="E37">A11</font></span></a>, <a class="txt" href="#E18:26"><span class="lab"><font color="Green" title="E44">A18</font></span></a>, <a class="ref" href="anproj_2.html#T6" target="_self" title="ANPROJ_2:th.6">Th6</a></span>;<br/>
<a NAME="E25:26"/><span class="lab"><font color="Green" title="E48">A22</font></span>: 
 not <font color="Maroon" title="c3">u</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E26:26"/><span class="lab"><font color="Green" title="E49">A23</font></span>: 
 not <font color="Maroon" title="c4">v</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E27:26"/><span class="lab"><font color="Green" title="E50">A24</font></span>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c7">v2</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &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="c4">v</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:26"><span class="lab"><font color="Green" title="E31">A5</font></span></a>, <a class="txt" href="#E12:26"><span class="lab"><font color="Green" title="E38">A12</font></span></a>, <a class="ref" href="anproj_2.html#D3" target="_self" title="ANPROJ_2:def.3">Def3</a>, <a class="ref" href="anproj_1.html#T11" title="ANPROJ_1:th.11">ANPROJ_1:11</a></span>;<br/>
<a NAME="E28:26"/><span class="lab"><font color="Green" title="E51">A25</font></span>: 
( <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;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:26"><span class="lab"><font color="Green" title="E31">A5</font></span></a>, <a class="txt" href="#E12:26"><span class="lab"><font color="Green" title="E38">A12</font></span></a>, <a class="ref" href="anproj_2.html#D3" target="_self" title="ANPROJ_2:def.3">Def3</a>, <a class="ref" href="anproj_1.html#T11" title="ANPROJ_1:th.11">ANPROJ_1:11</a></span>;<br/>
<a NAME="E29:26"/><span class="lab"><font color="Green" title="E52">A26</font></span>: 
 not <font color="Maroon" title="c6">u2</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E30:26"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c6">u2</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E25:26"><span class="lab"><font color="Green" title="E48">A22</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">a1</font>, <font color="Maroon" title="c15">b1</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E32:26"/><span class="lab"><font color="Green" title="E53">A27</font></span>: 
<font color="Maroon" title="c15">b1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u2</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">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E33:26"/><span class="lab"><font color="Green" title="E54">A28</font></span>: 
<font color="Maroon" title="c14">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E34:26"/><span class="lab"><font color="Green" title="E55">A29</font></span>: 
<font color="Maroon" title="c15">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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:26"><span class="lab"><font color="Green" title="E32">A6</font></span></a>, <a class="txt" href="#E9:26"><span class="lab"><font color="Green" title="E35">A9</font></span></a>, <a class="txt" href="#E28:26"><span class="lab"><font color="Green" title="E51">A25</font></span></a>, <a class="ref" href="anproj_2.html#T6" target="_self" title="ANPROJ_2:th.6">Th6</a></span>;<br/>
<a NAME="E35:26"/><span class="lab"><font color="Green" title="E56">A30</font></span>: 
 not <font color="Maroon" title="c7">v2</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E36:26"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c7">v2</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E26:26"><span class="lab"><font color="Green" title="E49">A23</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c16">a2</font>, <font color="Maroon" title="c17">b2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E38:26"/><span class="lab"><font color="Green" title="E57">A31</font></span>: 
<font color="Maroon" title="c17">b2</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">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E39:26"/><span class="lab"><font color="Green" title="E58">A32</font></span>: 
<font color="Maroon" title="c16">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E40:26"/><span class="lab"><font color="Green" title="E59">A33</font></span>: 
<font color="Maroon" title="c17">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:26"><span class="lab"><font color="Green" title="E33">A7</font></span></a>, <a class="txt" href="#E10:26"><span class="lab"><font color="Green" title="E36">A10</font></span></a>, <a class="txt" href="#E27:26"><span class="lab"><font color="Green" title="E50">A24</font></span></a>, <a class="ref" href="anproj_2.html#T6" target="_self" title="ANPROJ_2:th.6">Th6</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c18">u29</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">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c19">v29</font> = <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c20">w29</font> = <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>;<br/>
<a NAME="E41:26"/><span class="lab"><font color="Green" title="E60">A34</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:26"><span class="lab"><font color="Green" title="E57">A31</font></span></a>, <a class="txt" href="#E40:26"><span class="lab"><font color="Green" title="E59">A33</font></span></a>, <a class="txt" href="anproj_2.html#E19"><span class="lab"><font color="Green" title="E19">Lm9</font></span></a></span>;<br/>
<a NAME="E42:26"/><span class="lab"><font color="Green" title="E61">A35</font></span>: 
 not <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:26"><span class="lab"><font color="Green" title="E56">A30</font></span></a>, <a class="txt" href="#E38:26"><span class="lab"><font color="Green" title="E57">A31</font></span></a>, <a class="txt" href="#E40:26"><span class="lab"><font color="Green" title="E59">A33</font></span></a>, <a class="txt" href="anproj_2.html#E21"><span class="lab"><font color="Green" title="E21">Lm11</font></span></a></span>;<br/>
<a NAME="E43:26"/><span class="lab"><font color="Green" title="E62">A36</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c8">w2</font>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:26"><span class="lab"><font color="Green" title="E46">A20</font></span></a>, <a class="txt" href="#E24:26"><span class="lab"><font color="Green" title="E47">A21</font></span></a>, <a class="txt" href="anproj_2.html#E19"><span class="lab"><font color="Green" title="E19">Lm9</font></span></a></span>;<br/>
<a NAME="E44:26"/><span class="lab"><font color="Green" title="E63">A37</font></span>: 
( <font color="Maroon" title="c3">u</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;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:26"><span class="lab"><font color="Green" title="E38">A12</font></span></a>, <a class="txt" href="#E15:26"><span class="lab"><font color="Green" title="E41">A15</font></span></a>, <a class="ref" href="anproj_2.html#D2" target="_self" title="ANPROJ_2:def.2">Def2</a>, <a class="ref" href="anproj_1.html#T12" title="ANPROJ_1:th.12">ANPROJ_1:12</a></span>;<br/>
<a NAME="E45:26"/><span class="lab"><font color="Green" title="E64">A38</font></span>: 
 not <font color="Maroon" title="c11">w1</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E46:26"/><span class="kw">then </span>
<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:26"><span class="lab"><font color="Green" title="E48">A22</font></span></a>, <a class="txt" href="#E26:26"><span class="lab"><font color="Green" title="E49">A23</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c21">c3</font>, <font color="Maroon" title="c22">d3</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E48:26"/><span class="lab"><font color="Green" title="E65">A39</font></span>: 
<font color="Maroon" title="c11">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">c3</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="c22">d3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:26"><span class="lab"><font color="Green" title="E63">A37</font></span></a>, <a class="ref" href="anproj_2.html#T7" target="_self" title="ANPROJ_2:th.7">Th7</a></span>;<br/>
<a NAME="E49:26"/><span class="lab"><font color="Green" title="E66">A40</font></span>: 
 <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">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:26"><span class="lab"><font color="Green" title="E53">A27</font></span></a>, <a class="txt" href="#E34:26"><span class="lab"><font color="Green" title="E55">A29</font></span></a>, <a class="txt" href="anproj_2.html#E19"><span class="lab"><font color="Green" title="E19">Lm9</font></span></a></span>;<br/>
<a NAME="E50:26"/><span class="lab"><font color="Green" title="E67">A41</font></span>: 
( <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c9">u1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &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> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:26"><span class="lab"><font color="Green" title="E40">A14</font></span></a>, <a class="txt" href="#E15:26"><span class="lab"><font color="Green" title="E41">A15</font></span></a>, <a class="ref" href="anproj_2.html#D2" target="_self" title="ANPROJ_2:def.2">Def2</a>, <a class="ref" href="anproj_1.html#T12" title="ANPROJ_1:th.12">ANPROJ_1:12</a></span>;<br/>
<a NAME="E51:26"/><span class="lab"><font color="Green" title="E68">A42</font></span>: 
 not <font color="Maroon" title="c9">u1</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E52:26"/><span class="kw">then </span>
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c9">u1</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:26"><span class="lab"><font color="Green" title="E49">A23</font></span></a>, <a class="txt" href="#E17:26"><span class="lab"><font color="Green" title="E43">A17</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c23">c1</font>, <font color="Maroon" title="c24">d1</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E54:26"/><span class="lab"><font color="Green" title="E69">A43</font></span>: 
<font color="Maroon" title="c9">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">c1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</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="c24">d1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E50:26"><span class="lab"><font color="Green" title="E67">A41</font></span></a>, <a class="ref" href="anproj_2.html#T7" target="_self" title="ANPROJ_2:th.7">Th7</a></span>;<br/>
<a NAME="E55:26"/>
<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c8">w2</font>,<font color="Maroon" title="c9">u1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:26"><span class="lab"><font color="Green" title="E42">A16</font></span></a>, <a class="ref" href="anproj_2.html#D2" target="_self" title="ANPROJ_2:def.2">Def2</a></span>;<br/>
<a NAME="E56:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A44</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>,<font color="Maroon" title="c9">u1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:26"><span class="lab"><font color="Green" title="E60">A34</font></span></a>, <a class="txt" href="#E43:26"><span class="lab"><font color="Green" title="E62">A36</font></span></a>, <a class="ref" href="anproj_1.html#T4" title="ANPROJ_1:th.4">ANPROJ_1:4</a></span>;<br/>
<a NAME="E57:26"/><span class="lab"><font color="Green" title="E71">A45</font></span>: 
 not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:26"><span class="lab"><font color="Green" title="E40">A14</font></span></a>, <a class="txt" href="#E39:26"><span class="lab"><font color="Green" title="E58">A32</font></span></a>, <a class="txt" href="anproj_2.html#E20"><span class="lab"><font color="Green" title="E20">Lm10</font></span></a></span>;<br/>
<a NAME="E58:26"/><span class="lab"><font color="Green" title="E72">A46</font></span>: 
 not <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:26"><span class="lab"><font color="Green" title="E45">A19</font></span></a>, <a class="txt" href="#E22:26"><span class="lab"><font color="Green" title="E46">A20</font></span></a>, <a class="txt" href="#E24:26"><span class="lab"><font color="Green" title="E47">A21</font></span></a>, <a class="txt" href="anproj_2.html#E21"><span class="lab"><font color="Green" title="E21">Lm11</font></span></a></span>;<br/>
<a NAME="E59:26"/><span class="kw">then </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">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>,<font color="Maroon" title="c9">u1</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:26"><span class="lab"><font color="Green" title="E68">A42</font></span></a>, <a class="txt" href="#E42:26"><span class="lab"><font color="Green" title="E61">A35</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c25">A1</font>, <font color="Maroon" title="c26">B1</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E61:26"/><span class="lab"><font color="Green" title="E73">A47</font></span>: 
<font color="Maroon" title="c9">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c25">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="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</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="c26">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="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:26"><span class="lab"><font color="Green" title="E70">A44</font></span></a>, <a class="txt" href="#E57:26"><span class="lab"><font color="Green" title="E71">A45</font></span></a>, <a class="ref" href="anproj_2.html#T7" target="_self" title="ANPROJ_2:th.7">Th7</a></span>;<br/>
<a NAME="E62:26"/><span class="lab"><font color="Green" title="E74">A48</font></span>: 
( <font color="Maroon" title="c3">u</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>  &amp;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c5">w</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:26"><span class="lab"><font color="Green" title="E39">A13</font></span></a>, <a class="txt" href="#E15:26"><span class="lab"><font color="Green" title="E41">A15</font></span></a>, <a class="ref" href="anproj_2.html#D2" target="_self" title="ANPROJ_2:def.2">Def2</a>, <a class="ref" href="anproj_1.html#T12" title="ANPROJ_1:th.12">ANPROJ_1:12</a></span>;<br/>
<a NAME="E63:26"/><span class="lab"><font color="Green" title="E75">A49</font></span>: 
 not <font color="Maroon" title="c10">v1</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E64:26"/><span class="kw">then </span>
<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c10">v1</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:26"><span class="lab"><font color="Green" title="E48">A22</font></span></a>, <a class="txt" href="#E17:26"><span class="lab"><font color="Green" title="E43">A17</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c27">c2</font>, <font color="Maroon" title="c28">d2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E66:26"/><span class="lab"><font color="Green" title="E76">A50</font></span>: 
<font color="Maroon" title="c10">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c27">c2</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="c28">d2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E62:26"><span class="lab"><font color="Green" title="E74">A48</font></span></a>, <a class="ref" href="anproj_2.html#T7" target="_self" title="ANPROJ_2:th.7">Th7</a></span>;<br/>
<a NAME="E67:26"/><span class="lab"><font color="Green" title="E77">A51</font></span>: 
<font color="Maroon" title="c9">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c25">A1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c26">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="c25">A1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">a2</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</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="c26">B1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a3</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E61:26"><span class="lab"><font color="Green" title="E73">A47</font></span></a>, <a class="txt" href="anproj_2.html#E22"><span class="lab"><font color="Green" title="E22">Lm12</font></span></a></span>;<br/>
<a NAME="E68:26"/>
<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:26"><span class="lab"><font color="Green" title="E42">A16</font></span></a>, <a class="ref" href="anproj_2.html#D2" target="_self" title="ANPROJ_2:def.2">Def2</a></span>;<br/>
<a NAME="E69:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E78">A52</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">a1</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">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span>,<font color="Maroon" title="c11">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:26"><span class="lab"><font color="Green" title="E66">A40</font></span></a>, <a class="txt" href="#E41:26"><span class="lab"><font color="Green" title="E60">A34</font></span></a>, <a class="ref" href="anproj_1.html#T4" title="ANPROJ_1:th.4">ANPROJ_1:4</a></span>;<br/>
<a NAME="E70:26"/><span class="lab"><font color="Green" title="E79">A53</font></span>: 
 not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">a1</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">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:26"><span class="lab"><font color="Green" title="E38">A12</font></span></a>, <a class="txt" href="#E33:26"><span class="lab"><font color="Green" title="E54">A28</font></span></a>, <a class="txt" href="anproj_2.html#E20"><span class="lab"><font color="Green" title="E20">Lm10</font></span></a></span>;<br/>
<a NAME="E71:26"/><span class="lab"><font color="Green" title="E80">A54</font></span>: 
 not <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:26"><span class="lab"><font color="Green" title="E52">A26</font></span></a>, <a class="txt" href="#E32:26"><span class="lab"><font color="Green" title="E53">A27</font></span></a>, <a class="txt" href="#E34:26"><span class="lab"><font color="Green" title="E55">A29</font></span></a>, <a class="txt" href="anproj_2.html#E21"><span class="lab"><font color="Green" title="E21">Lm11</font></span></a></span>;<br/>
<a NAME="E72:26"/><span class="kw">then </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">a1</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">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span>,<font color="Maroon" title="c11">w1</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E45:26"><span class="lab"><font color="Green" title="E64">A38</font></span></a>, <a class="txt" href="#E42:26"><span class="lab"><font color="Green" title="E61">A35</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c29">A3</font>, <font color="Maroon" title="c30">B3</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E74:26"/><span class="lab"><font color="Green" title="E81">A55</font></span>: 
<font color="Maroon" title="c11">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c29">A3</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">a1</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="c30">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">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E69:26"><span class="lab"><font color="Green" title="E78">A52</font></span></a>, <a class="txt" href="#E70:26"><span class="lab"><font color="Green" title="E79">A53</font></span></a>, <a class="ref" href="anproj_2.html#T7" target="_self" title="ANPROJ_2:th.7">Th7</a></span>;<br/>
<a NAME="E75:26"/>
<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c8">w2</font>,<font color="Maroon" title="c10">v1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:26"><span class="lab"><font color="Green" title="E42">A16</font></span></a>, <a class="ref" href="anproj_2.html#D2" target="_self" title="ANPROJ_2:def.2">Def2</a></span>;<br/>
<a NAME="E76:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A56</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>,<font color="Maroon" title="c10">v1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:26"><span class="lab"><font color="Green" title="E66">A40</font></span></a>, <a class="txt" href="#E43:26"><span class="lab"><font color="Green" title="E62">A36</font></span></a>, <a class="ref" href="anproj_1.html#T4" title="ANPROJ_1:th.4">ANPROJ_1:4</a></span>;<br/>
<a NAME="E77:26"/><span class="lab"><font color="Green" title="E83">A57</font></span>: 
 not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:26"><span class="lab"><font color="Green" title="E39">A13</font></span></a>, <a class="txt" href="#E33:26"><span class="lab"><font color="Green" title="E54">A28</font></span></a>, <a class="txt" href="anproj_2.html#E20"><span class="lab"><font color="Green" title="E20">Lm10</font></span></a></span>;<br/>
<a NAME="E78:26"/><span class="lab"><font color="Green" title="E84">A58</font></span>: 
<font color="Maroon" title="c11">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c29">A3</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c30">B3</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="c29">A3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">a1</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="c30">B3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c16">a2</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:26"><span class="lab"><font color="Green" title="E81">A55</font></span></a>, <a class="txt" href="anproj_2.html#E22"><span class="lab"><font color="Green" title="E22">Lm12</font></span></a></span>;<br/>
<a NAME="E79:26"/>
<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">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span>,<font color="Maroon" title="c2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>,<font color="Maroon" title="c10">v1</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E63:26"><span class="lab"><font color="Green" title="E75">A49</font></span></a>, <a class="txt" href="#E71:26"><span class="lab"><font color="Green" title="E80">A54</font></span></a>, <a class="txt" href="#E58:26"><span class="lab"><font color="Green" title="E72">A46</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c31">A2</font>, <font color="Maroon" title="c32">B2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E81:26"/><span class="lab"><font color="Green" title="E85">A59</font></span>: 
<font color="Maroon" title="c10">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c31">A2</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">a1</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="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="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E76:26"><span class="lab"><font color="Green" title="E82">A56</font></span></a>, <a class="txt" href="#E77:26"><span class="lab"><font color="Green" title="E83">A57</font></span></a>, <a class="ref" href="anproj_2.html#T7" target="_self" title="ANPROJ_2:th.7">Th7</a></span>;<br/>
<a NAME="E82:26"/><span class="lab"><font color="Green" title="E86">A60</font></span>: 
<font color="Maroon" title="c10">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c31">A2</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c32">B2</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="c31">A2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">a1</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="c32">B2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">a3</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E81:26"><span class="lab"><font color="Green" title="E85">A59</font></span></a>, <a class="txt" href="anproj_2.html#E22"><span class="lab"><font color="Green" title="E22">Lm12</font></span></a></span>;<br/>
<a NAME="E83:26"/>
<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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">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="c21">c3</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="c22">d3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:26"><span class="lab"><font color="Green" title="E65">A39</font></span></a>, <a class="txt" href="anproj_2.html#E23"><span class="lab"><font color="Green" title="E23">Lm13</font></span></a></span>;<br/>
<a NAME="E84:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E87">A61</font></span>: 
<font color="Maroon" title="c29">A3</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c30">B3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:26"><span class="lab"><font color="Green" title="E38">A12</font></span></a>, <a class="txt" href="#E78:26"><span class="lab"><font color="Green" title="E84">A58</font></span></a>, <a class="ref" href="anproj_1.html#T8" title="ANPROJ_1:th.8">ANPROJ_1:8</a></span>;<br/>
<a NAME="E85:26"/>
<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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">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="c23">c1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</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="c24">d1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E54:26"><span class="lab"><font color="Green" title="E69">A43</font></span></a>, <a class="txt" href="anproj_2.html#E23"><span class="lab"><font color="Green" title="E23">Lm13</font></span></a></span>;<br/>
<a NAME="E86:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A62</font></span>: 
<font color="Maroon" title="c25">A1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c26">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:26"><span class="lab"><font color="Green" title="E40">A14</font></span></a>, <a class="txt" href="#E67:26"><span class="lab"><font color="Green" title="E77">A51</font></span></a>, <a class="ref" href="anproj_1.html#T8" title="ANPROJ_1:th.8">ANPROJ_1:8</a></span>;<br/>
<a NAME="E87:26"/>
<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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">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="c27">c2</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="c28">d2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E66:26"><span class="lab"><font color="Green" title="E76">A50</font></span></a>, <a class="txt" href="anproj_2.html#E23"><span class="lab"><font color="Green" title="E23">Lm13</font></span></a></span>;<br/>
<a NAME="E88:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A63</font></span>: 
<font color="Maroon" title="c31">A2</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c32">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:26"><span class="lab"><font color="Green" title="E39">A13</font></span></a>, <a class="txt" href="#E82:26"><span class="lab"><font color="Green" title="E86">A60</font></span></a>, <a class="ref" href="anproj_1.html#T8" title="ANPROJ_1:th.8">ANPROJ_1:8</a></span>;<br/>
<a NAME="E89:26"/><span class="lab"><font color="Green" title="E90">A64</font></span>: 
( <font color="Maroon" title="c25">A1</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="c31">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="c29">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>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E91">A65</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:26_1_1"/>
<font color="Maroon" title="c31">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:26_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E81:26"><span class="lab"><font color="Green" title="E85">A59</font></span></a>, <a class="txt" href="#E88:26"><span class="lab"><font color="Green" title="E89">A63</font></span></a>, <a class="txt" href="anproj_2.html#E24"><span class="lab"><font color="Green" title="E24">Lm14</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:26_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E63:26"><span class="lab"><font color="Green" title="E75">A49</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E92">A66</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:26_1_2"/>
<font color="Maroon" title="c25">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:26_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E61:26"><span class="lab"><font color="Green" title="E73">A47</font></span></a>, <a class="txt" href="#E86:26"><span class="lab"><font color="Green" title="E88">A62</font></span></a>, <a class="txt" href="anproj_2.html#E24"><span class="lab"><font color="Green" title="E24">Lm14</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:26_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:26"><span class="lab"><font color="Green" title="E68">A42</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E93">A67</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:26_1_3"/>
<font color="Maroon" title="c29">A3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:26_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c11">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:26"><span class="lab"><font color="Green" title="E81">A55</font></span></a>, <a class="txt" href="#E84:26"><span class="lab"><font color="Green" title="E87">A61</font></span></a>, <a class="txt" href="anproj_2.html#E24"><span class="lab"><font color="Green" title="E24">Lm14</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:26_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E45:26"><span class="lab"><font color="Green" title="E64">A38</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E4:26_1"/>
(  not <font color="Maroon" title="c25">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  not <font color="Maroon" title="c31">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>  or  not <font color="Maroon" title="c29">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>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E5:26_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26_1"><span class="lab"><font color="Green" title="E92">A66</font></span></a>, <a class="txt" href="#E1:26_1"><span class="lab"><font color="Green" title="E91">A65</font></span></a>, <a class="txt" href="#E3:26_1"><span class="lab"><font color="Green" title="E93">A67</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">set </span><font color="Maroon" title="c33">u19</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c34">v19</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c35">w19</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span>;<br/>
<a NAME="E90:26"/>
<font color="Maroon" title="c26">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c25">A1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E86:26"><span class="lab"><font color="Green" title="E88">A62</font></span></a></span>;<br/>
<a NAME="E91:26"/><span class="kw">then </span>
<font color="Maroon" title="c9">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">A1</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="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E67:26"><span class="lab"><font color="Green" title="E77">A51</font></span></a>, <a class="txt" href="anproj_2.html#E25"><span class="lab"><font color="Green" title="E25">Lm15</font></span></a></span>;<br/>
<a NAME="E92:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E91">A68</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>,<font color="Maroon" title="c9">u1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E89:26"><span class="lab"><font color="Green" title="E90">A64</font></span></a>, <a class="txt" href="anproj_2.html#E19"><span class="lab"><font color="Green" title="E19">Lm9</font></span></a></span>;<br/>
<a NAME="E93:26"/>
<font color="Maroon" title="c30">B3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c29">A3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E84:26"><span class="lab"><font color="Green" title="E87">A61</font></span></a></span>;<br/>
<a NAME="E94:26"/><span class="kw">then </span>
<font color="Maroon" title="c11">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">A3</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="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E78:26"><span class="lab"><font color="Green" title="E84">A58</font></span></a>, <a class="txt" href="anproj_2.html#E25"><span class="lab"><font color="Green" title="E25">Lm15</font></span></a></span>;<br/>
<a NAME="E95:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E92">A69</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span>,<font color="Maroon" title="c11">w1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E89:26"><span class="lab"><font color="Green" title="E90">A64</font></span></a>, <a class="txt" href="anproj_2.html#E19"><span class="lab"><font color="Green" title="E19">Lm9</font></span></a></span>;<br/>
<a NAME="E96:26"/>
<font color="Maroon" title="c32">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c31">A2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E88:26"><span class="lab"><font color="Green" title="E89">A63</font></span></a></span>;<br/>
<a NAME="E97:26"/><span class="kw">then </span>
<font color="Maroon" title="c10">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c31">A2</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="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E82:26"><span class="lab"><font color="Green" title="E86">A60</font></span></a>, <a class="txt" href="anproj_2.html#E25"><span class="lab"><font color="Green" title="E25">Lm15</font></span></a></span>;<br/>
<a NAME="E98:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E93">A70</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>,<font color="Maroon" title="c10">v1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E89:26"><span class="lab"><font color="Green" title="E90">A64</font></span></a>, <a class="txt" href="anproj_2.html#E19"><span class="lab"><font color="Green" title="E19">Lm9</font></span></a></span>;<br/>
<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"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</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"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</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">1 <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="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</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"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</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">1 <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="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D8" title="RLVECT_1:def.8">RLVECT_1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</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"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</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"><font color="Maroon" title="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D8" title="RLVECT_1:def.8">RLVECT_1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</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"><font color="Maroon" title="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T16" title="RLVECT_1:th.16">RLVECT_1:16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</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">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span></span>)</span></span>)</span></span>)</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="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T33" title="RLVECT_1:th.33">RLVECT_1:33</a></span>
<br/>.= 
<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="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span></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="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c14">a1</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"><span class="p2">(<span class="default"><font color="Maroon" title="c14">a1</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="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" title="RLVECT_1:def.3">RLVECT_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</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"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</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="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</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"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c14">a1</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"><span class="p2">(<span class="default"><font color="Maroon" title="c14">a1</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="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" title="RLVECT_1:def.3">RLVECT_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c14">a1</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"><span class="p2">(<span class="default"><font color="Maroon" title="c14">a1</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="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T5" title="RLVECT_1:th.5">RLVECT_1:5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c14">a1</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"><span class="p2">(<span class="default"><font color="Maroon" title="c14">a1</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="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T4" title="RLVECT_1:th.4">RLVECT_1:4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></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="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c14">a1</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"><span class="p3">(<span class="default"><font color="Maroon" title="c14">a1</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="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" title="RLVECT_1:def.3">RLVECT_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></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"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c14">a1</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="c14">a1</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"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" title="RLVECT_1:def.3">RLVECT_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></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="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="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T5" title="RLVECT_1:th.5">RLVECT_1:5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T4" title="RLVECT_1:th.4">RLVECT_1:4</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T5" title="RLVECT_1:th.5">RLVECT_1:5</a></span>
;<br/>
<a NAME="E100:26"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a3</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_1.html#D2" title="ANPROJ_1:def.2">ANPROJ_1:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E101:26"/>
<font color="Maroon" title="c9">u1</font>,<font color="Maroon" title="c10">v1</font>,<font color="Maroon" title="c11">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E92:26"><span class="lab"><font color="Green" title="E91">A68</font></span></a>, <a class="txt" href="#E98:26"><span class="lab"><font color="Green" title="E93">A70</font></span></a>, <a class="txt" href="#E95:26"><span class="lab"><font color="Green" title="E92">A69</font></span></a>, <a class="ref" href="anproj_1.html#T4" title="ANPROJ_1:th.4">ANPROJ_1:4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
