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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">v</font>, <font color="Olive" title="b5">u1</font>, <font color="Olive" title="b6">v1</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">v</font>,<font color="Olive" title="b5">u1</font>,<font color="Olive" title="b6">v1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font> holds <br/><font color="Olive" title="b4">v</font>,<font color="Olive" title="b3">u</font>,<font color="Olive" title="b6">v1</font>,<font color="Olive" title="b5">u1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_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">v</font>, <font color="Maroon" title="c6">u1</font>, <font color="Maroon" title="c7">v1</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">v</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> implies <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_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="E1:35"/><i><font color="Green" title="E33">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="E2:35"/><i><font color="Green" title="E34">A2</font></i>: 
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_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="c5">v</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font></span><br/>

<a NAME="E3:35"/><i><font color="Green" title="E35">A3</font></i>: 
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">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="geomtrap.html#E2:35"><i><font color="Green" title="E34">A2</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">u</font>, <font color="Maroon" title="c9">u'</font>, <font color="Maroon" title="c10">v</font>, <font color="Maroon" title="c11">v'</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"> ( <font color="Maroon" title="c8">u</font>,<font color="Maroon" title="c9">u'</font>,<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c11">v'</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> implies <font color="Maroon" title="c9">u'</font>,<font color="Maroon" title="c8">u</font>,<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c11">v'</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )</span><br/><b>assume </b><a NAME="E1:35_1"/>
<font color="Maroon" title="c8">u</font>,<font color="Maroon" title="c9">u'</font>,<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c11">v'</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">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="c9">u'</font>,<font color="Maroon" title="c8">u</font>,<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c11">v'</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font></span><br/><a NAME="E2:35_1"/><b>then </b>
<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c11">v'</font>,<font color="Maroon" title="c8">u</font>,<font color="Maroon" title="c9">u'</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">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="geomtrap.html#E1:35"><i><font color="Green" title="E33">A1</font></i></a>, <a class="txt" href="geomtrap.html#E23"><i><font color="Green" title="E20">Lm4A</font></i></a></i>;<br/><a NAME="E3:35_1"/><b>then </b>
<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c11">v'</font>,<font color="Maroon" title="c9">u'</font>,<font color="Maroon" title="c8">u</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">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="geomtrap.html#E1:35"><i><font color="Green" title="E33">A1</font></i></a>, <a class="txt" href="geomtrap.html#E22"><i><font color="Green" title="E19">Lm4</font></i></a></i>;<br/><b>hence </b><a NAME="E4:35_1"/>
<font color="Maroon" title="c9">u'</font>,<font color="Maroon" title="c8">u</font>,<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c11">v'</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">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="geomtrap.html#E1:35"><i><font color="Green" title="E33">A1</font></i></a>, <a class="txt" href="geomtrap.html#E23"><i><font color="Green" title="E20">Lm4A</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/></div><b>end;</b></div>
<a NAME="E5:35"/><b>then </b>
( <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c6">u1</font> &amp; <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">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="geomtrap.html#E3:35"><i><font color="Green" title="E35">A3</font></i></a>, <a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</a></i>;<br/>
<b>hence </b><a NAME="E6:35"/>
<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</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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