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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">w</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">u1</font>, <font color="Olive" title="b5">u2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  st  <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b5">u2</font> <a href="analmetr.html#R2" title="ANALMETR:pred.2">are_Ort_wrt</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b4">u1</font>,<font color="Olive" title="b5">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b3">u</font> <a href="analmetr.html#R2" title="ANALMETR:pred.2">are_Ort_wrt</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font> holds <br/><font color="Olive" title="b5">u2</font>,<font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b4">u1</font> <a href="analmetr.html#R2" title="ANALMETR:pred.2">are_Ort_wrt</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font></span><br/><b>let </b><font color="Maroon" title="c2">w</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">u</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <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> &amp; <font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c6">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</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> implies <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <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> )</span><br/>











<b>assume </b><b>that </b><br/><a NAME="E1:19"/><i><font color="Green" title="E19">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="E2:19"/><i><font color="Green" title="E20">X</font></i>: 
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <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="E3:19"/><i><font color="Green" title="E21">A2</font></i>: 
<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c6">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <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></span><br/>

<b>consider </b><font color="Maroon" title="c7">a1</font>, <font color="Maroon" title="c8">a2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E5:19"/><i><font color="Green" title="E22">A3</font></i>: 
<font color="Maroon" title="c4">u</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#K1" title="RLVECT_1:func.1">*</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#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span>
 <b>by </b><i><a class="txt" href="analmetr.html#E1:19"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="analmetr.html#D1" target="_self" title="ANALMETR:def.1">Def1</a></i>;<br/>
<b>consider </b><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="E7:19"/><i><font color="Green" title="E23">A4</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#K1" title="RLVECT_1:func.1">*</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#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span>
 <b>by </b><i><a class="txt" href="analmetr.html#E1:19"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="analmetr.html#D1" target="_self" title="ANALMETR:def.1">Def1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c11">c1</font>, <font color="Maroon" title="c12">c2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E9:19"/><i><font color="Green" title="E24">A5</font></i>: 
<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="c11">c1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</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">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span>
 <b>by </b><i><a class="txt" href="analmetr.html#E1:19"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="analmetr.html#D1" target="_self" title="ANALMETR:def.1">Def1</a></i>;<br/>
<a NAME="E10:19"/><i><font color="Green" title="E25">A6</font></i>: 
<font color="Maroon" title="c5">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</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="c9">b1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">c1</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</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#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">c2</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span>
 
<b>by </b><i><a class="txt" href="analmetr.html#E7:19"><i><font color="Green" title="E23">A4</font></i></a>, <a class="txt" href="analmetr.html#E9:19"><i><font color="Green" title="E24">A5</font></i></a>, <a class="txt" href="analmetr.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E11:19"/><i><font color="Green" title="E26">B6</font></i>: 
<font color="Maroon" title="c6">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</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="c11">c1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c7">a1</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</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="c12">c2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c8">a2</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span>
 
<b>by </b><i><a class="txt" href="analmetr.html#E5:19"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="analmetr.html#E9:19"><i><font color="Green" title="E24">A5</font></i></a>, <a class="txt" href="analmetr.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E12:19"/><i><font color="Green" title="E27">C6</font></i>: 
<font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u1</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="c7">a1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c9">b1</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</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="c8">a2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c10">b2</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span>
 
<b>by </b><i><a class="txt" href="analmetr.html#E5:19"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="analmetr.html#E7:19"><i><font color="Green" title="E23">A4</font></i></a>, <a class="txt" href="analmetr.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E13:19"/><i><font color="Green" title="E28">A7</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> <span class="p2">(<span class="default"><font color="Maroon" title="c9">b1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">c1</font></span>)</span></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> <span class="p2">(<span class="default"><font color="Maroon" title="c10">b2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">c2</font></span>)</span></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#E10:19"><i><font color="Green" title="E25">A6</font></i></a>, <a class="txt" href="analmetr.html#E1:19"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="analmetr.html#T5" target="_self" title="ANALMETR:th.5">Th5</a>, <a class="txt" href="analmetr.html#E2:19"><i><font color="Green" title="E20">X</font></i></a>, <a class="txt" href="analmetr.html#E5:19"><i><font color="Green" title="E22">A3</font></i></a></i>;<br/>
<a NAME="E14:19"/>
<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> <span class="p2">(<span class="default"><font color="Maroon" title="c11">c1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c7">a1</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">b2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">c2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c8">a2</font></span>)</span></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#E1:19"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="analmetr.html#E3:19"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="analmetr.html#E7:19"><i><font color="Green" title="E23">A4</font></i></a>, <a class="ref" href="analmetr.html#T5" target="_self" title="ANALMETR:th.5">Th5</a>, <a class="txt" href="analmetr.html#E11:19"><i><font color="Green" title="E26">B6</font></i></a></i>;<br/>
<a NAME="E15:19"/><b>then </b>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">c1</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#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c9">b1</font></span>)</span></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">c2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">a2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c10">b2</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="analmetr.html#E13:19"><i><font color="Green" title="E28">A7</font></i></a></i>;<br/>
<b>hence </b><a NAME="E16:19"/>
<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <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>by </b><i><a class="txt" href="analmetr.html#E9:19"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="analmetr.html#D2" target="_self" title="ANALMETR:def.2">Def2</a>, <a class="txt" href="analmetr.html#E12:19"><i><font color="Green" title="E27">C6</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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