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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">w</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">v</font>, <font color="Maroon" title="c5">u1</font>, <font color="Maroon" title="c6">u2</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:16"/><i><font color="Green" title="E16">A1</font></i>: 
 <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 <b>and </b><br/><a NAME="E2:16"/><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> <a href="analmetr.html#R2" title="ANALMETR:pred.2">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 <b>and </b><br/><a NAME="E3:16"/><i><font color="Green" title="E18">A3</font></i>: 
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> <a href="analmetr.html#R2" title="ANALMETR:pred.2">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 <b>and </b><br/><a NAME="E4:16"/><i><font color="Green" title="E19">A4</font></i>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c7">a1</font>, <font color="Maroon" title="c8">a2</font>, <font color="Maroon" title="c9">b1</font>, <font color="Maroon" title="c10">b2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E6:16"/><i><font color="Green" title="E20">A5</font></i>: 
( <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">a1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">w</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="c8">a2</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">y</font></span>)</span> &amp; <font color="Maroon" title="c5">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">b1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">w</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="c10">b2</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">y</font></span>)</span> )
 <b>and </b><br/><a NAME="E7:16"/><i><font color="Green" title="E21">A6</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">a1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">b1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c10">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="analmetr.html#E2:16"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="analmetr.html#D2" target="_self" title="ANALMETR:def.2">Def2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c11">a1'</font>, <font color="Maroon" title="c12">a2'</font>, <font color="Maroon" title="c13">c1</font>, <font color="Maroon" title="c14">c2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E9:16"/><i><font color="Green" title="E22">A7</font></i>: 
( <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">a1'</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">w</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="c12">a2'</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">y</font></span>)</span> &amp; <font color="Maroon" title="c6">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">c1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">w</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="c14">c2</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">y</font></span>)</span> )
 <b>and </b><br/><a NAME="E10:16"/><i><font color="Green" title="E23">A8</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">a1'</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c13">c1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a2'</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="analmetr.html#E3:16"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="analmetr.html#D2" target="_self" title="ANALMETR:def.2">Def2</a></i>;<br/>
<a NAME="E11:16"/><i><font color="Green" title="E24">A9</font></i>: 
( <font color="Maroon" title="c7">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a1'</font> &amp; <font color="Maroon" title="c8">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">a2'</font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E1:16"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="analmetr.html#E6:16"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="analmetr.html#E9:16"><i><font color="Green" title="E22">A7</font></i></a>, <a class="txt" href="analmetr.html#E6"><i><font color="Green" title="E6">Lm4</font></i></a></i>;<br/>
<div><i><font color="Green" title="E25">A10</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1"/><i><font color="Green" title="E26">A11</font></i>: 
<font color="Maroon" title="c7">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><a NAME="E2:16_1"/><b>then </b><i><font color="Green" title="E27">A12</font></i>: 
<font color="Maroon" title="c8">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> 
 <b>by </b><i><a class="txt" href="analmetr.html#E4:16"><i><font color="Green" title="E19">A4</font></i></a>, <a class="txt" href="analmetr.html#E6:16"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="analmetr.html#E2"><i><font color="Green" title="E2">Lm2</font></i></a></i>;<br/><a NAME="E3:16_1"/><b>then </b><i><font color="Green" title="E28">A13</font></i>: 
<font color="Maroon" title="c14">c2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="analmetr.html#E10:16"><i><font color="Green" title="E23">A8</font></i></a>, <a class="txt" href="analmetr.html#E11:16"><i><font color="Green" title="E24">A9</font></i></a>, <a class="txt" href="analmetr.html#E1:16_1"><i><font color="Green" title="E26">A11</font></i></a>, <a class="ref" href="xcmplx_1.html#T6" title="XCMPLX_1:th.6">XCMPLX_1:6</a></i>;<br/><a NAME="E4:16_1"/>
<font color="Maroon" title="c10">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="analmetr.html#E7:16"><i><font color="Green" title="E21">A6</font></i></a>, <a class="txt" href="analmetr.html#E1:16_1"><i><font color="Green" title="E26">A11</font></i></a>, <a class="txt" href="analmetr.html#E2:16_1"><i><font color="Green" title="E27">A12</font></i></a>, <a class="ref" href="xcmplx_1.html#T6" title="XCMPLX_1:th.6">XCMPLX_1:6</a></i>;<br/><a NAME="E5:16_1"/><b>then </b><i><font color="Green" title="E29">A14</font></i>: 
( <font color="Maroon" title="c5">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">b1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">w</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span> &amp; <font color="Maroon" title="c6">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">c1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">w</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span> )
 <b>by </b><i><a class="txt" href="analmetr.html#E6:16"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="analmetr.html#E9:16"><i><font color="Green" title="E22">A7</font></i></a>, <a class="txt" href="analmetr.html#E3:16_1"><i><font color="Green" title="E28">A13</font></i></a>, <a class="ref" href="rlvect_1.html#T23" title="RLVECT_1:th.23">RLVECT_1:23</a></i>;<br/><a NAME="E6:16_1"/><b>then </b><i><font color="Green" title="E30">A15</font></i>: 
( <font color="Maroon" title="c5">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">w</font> &amp; <font color="Maroon" title="c6">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">w</font> )
 <b>by </b><i><a class="ref" href="rlvect_1.html#T10" title="RLVECT_1:th.10">RLVECT_1:10</a></i>;<br/><i><font color="Green" title="E31">A16</font></i>: <font color="Maroon" title="c13">c1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">u1</font> = 
<font color="Maroon" title="c13">c1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">b1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">w</font></span>)</span>
<b>by </b><i><a class="txt" href="analmetr.html#E5:16_1"><i><font color="Green" title="E29">A14</font></i></a>, <a class="ref" href="rlvect_1.html#T10" title="RLVECT_1:th.10">RLVECT_1:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">b1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c13">c1</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">w</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9" title="RLVECT_1:def.9">RLVECT_1:def 9</a></i>
<br/>.= 
<font color="Maroon" title="c9">b1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c6">u2</font>
<b>by </b><i><a class="txt" href="analmetr.html#E6:16_1"><i><font color="Green" title="E30">A15</font></i></a>, <a class="ref" href="rlvect_1.html#D9" title="RLVECT_1:def.9">RLVECT_1:def 9</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1_2"/>
<font color="Maroon" title="c9">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><b>then </b>1 <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">u1</font> = 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">w</font>
<b>by </b><i><a class="txt" href="analmetr.html#E6:16_1"><i><font color="Green" title="E30">A15</font></i></a>, <a class="ref" href="rlvect_1.html#D9" title="RLVECT_1:def.9">RLVECT_1:def 9</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T23" title="RLVECT_1:th.23">RLVECT_1:23</a></i>
<br/>.= 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c6">u2</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T23" title="RLVECT_1:th.23">RLVECT_1:23</a></i>
;<br/><b>hence </b><a NAME="E3:16_1_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <font color="Olive" title="b1">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c6">u2</font> &amp; ( <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E9:16_1"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <font color="Olive" title="b1">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c6">u2</font> &amp; ( <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 <b>by </b><i><a class="txt" href="analmetr.html#E7:16_1"><i><font color="Green" title="E31">A16</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2"/><i><font color="Green" title="E26">A17</font></i>: 
<font color="Maroon" title="c7">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> 
 ;<br/><i><font color="Green" title="E27">A18</font></i>: <font color="Maroon" title="c9">b1</font> = 
1 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">b1</font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">a1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">a1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">b1</font>
<b>by </b><i><a class="txt" href="analmetr.html#E1:16_2"><i><font color="Green" title="E26">A17</font></i></a>, <a class="ref" href="xcmplx_0.html#D7" title="XCMPLX_0:def.7">XCMPLX_0:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">a1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">b1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">a1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c8">a2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c10">b2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">a1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="analmetr.html#E7:16"><i><font color="Green" title="E21">A6</font></i></a></i>
;<br/><i><font color="Green" title="E28">A19</font></i>: <font color="Maroon" title="c13">c1</font> = 
1 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c13">c1</font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">a1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">a1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c13">c1</font>
<b>by </b><i><a class="txt" href="analmetr.html#E1:16_2"><i><font color="Green" title="E26">A17</font></i></a>, <a class="ref" href="xcmplx_0.html#D7" title="XCMPLX_0:def.7">XCMPLX_0:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">a1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c13">c1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">a1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c8">a2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">a1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="analmetr.html#E10:16"><i><font color="Green" title="E23">A8</font></i></a>, <a class="txt" href="analmetr.html#E11:16"><i><font color="Green" title="E24">A9</font></i></a></i>
;<br/><a NAME="E4:16_2"/><b>then </b><i><font color="Green" title="E29">A20</font></i>: 
<font color="Maroon" title="c10">b2</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c6">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c8">a2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">a1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">w</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"><font color="Maroon" title="c10">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c2</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">y</font></span>)</span>
 <b>by </b><i><a class="txt" href="analmetr.html#E9:16"><i><font color="Green" title="E22">A7</font></i></a>, <a class="txt" href="analmetr.html#E3"><i><font color="Green" title="E3">Lm3</font></i></a></i>;<br/><a NAME="E5:16_2"/><i><font color="Green" title="E30">A21</font></i>: 
<font color="Maroon" title="c14">c2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c8">a2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c10">b2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">a1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c8">a2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c14">c2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">a1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span>
 ;<br/><div><i><font color="Green" title="E31">A22</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2_3"/><i><font color="Green" title="E32">A23</font></i>: 
( <font color="Maroon" title="c14">c2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c10">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ;<br/><b>take </b><font color="Maroon" title="c15">a</font> = <font color="Maroon" title="c14">c2</font>;<br/><b>take </b><font color="Maroon" title="c16">b</font> = <font color="Maroon" title="c10">b2</font>;<br/><b>thus </b><a NAME="E2:16_2_3"/>
( <font color="Maroon" title="c15">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c6">u2</font> &amp; ( <font color="Maroon" title="c15">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c16">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 <b>by </b><i><a class="txt" href="analmetr.html#E6:16"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="analmetr.html#E2:16_2"><i><font color="Green" title="E27">A18</font></i></a>, <a class="txt" href="analmetr.html#E4:16_2"><i><font color="Green" title="E29">A20</font></i></a>, <a class="txt" href="analmetr.html#E5:16_2"><i><font color="Green" title="E30">A21</font></i></a>, <a class="txt" href="analmetr.html#E1:16_2_3"><i><font color="Green" title="E32">A23</font></i></a>, <a class="txt" href="analmetr.html#E3"><i><font color="Green" title="E3">Lm3</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2_4"/>
( <font color="Maroon" title="c10">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c14">c2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ;<br/><a NAME="E2:16_2_4"/><b>then </b>
1 <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c6">u2</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E6:16"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="analmetr.html#E9:16"><i><font color="Green" title="E22">A7</font></i></a>, <a class="txt" href="analmetr.html#E2:16_2"><i><font color="Green" title="E27">A18</font></i></a>, <a class="txt" href="analmetr.html#E3:16_2"><i><font color="Green" title="E28">A19</font></i></a></i>;<br/><b>hence </b><a NAME="E3:16_2_4"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <font color="Olive" title="b1">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c6">u2</font> &amp; ( <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:16_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <font color="Olive" title="b1">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c6">u2</font> &amp; ( <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 <b>by </b><i><a class="txt" href="analmetr.html#E6:16_2"><i><font color="Green" title="E31">A22</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E14:16"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <font color="Olive" title="b1">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c6">u2</font> &amp; ( <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 <b>by </b><i><a class="txt" href="analmetr.html#E12:16"><i><font color="Green" title="E25">A10</font></i></a></i>;<br/>


</div>
