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<div class="add">

<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> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>;<br/><b>let </b><font color="Maroon" title="c4">u</font>, <font color="Maroon" title="c5">u'</font>, <font color="Maroon" title="c6">u1</font>, <font color="Maroon" title="c7">u2</font>, <font color="Maroon" title="c8">v1</font>, <font color="Maroon" title="c9">v2</font>, <font color="Maroon" title="c10">t1</font>, <font color="Maroon" title="c11">t2</font>, <font color="Maroon" title="c12">w1</font>, <font color="Maroon" title="c13">w2</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="E1:66"/><i><font color="Green" title="E62">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="E2:66"/><i><font color="Green" title="E63">A2</font></i>: 
<font color="Maroon" title="c4">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">u'</font>
 <b>and </b><br/><a NAME="E3:66"/><i><font color="Green" title="E64">A3</font></i>: 
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c10">t1</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> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c7">u2</font>,<font color="Maroon" title="c11">t2</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> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c8">v1</font>,<font color="Maroon" title="c12">w1</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> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c13">w2</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>and </b><br/><a NAME="E4:66"/><i><font color="Green" title="E65">A4</font></i>: 
<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">u2</font>,<font color="Maroon" title="c8">v1</font>,<font color="Maroon" title="c9">v2</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>
 ;<br/>

<a NAME="E5:66"/><i><font color="Green" title="E66">A5</font></i>: 
<font color="Maroon" title="c10">t1</font>,<font color="Maroon" title="c11">t2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c12">w1</font>,<font color="Maroon" title="c13">w2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1"><b>proof </b></a><div class="add">

<a NAME="E1:66_1"/>
<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">u2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c8">v1</font>,<font color="Maroon" title="c9">v2</font>
 
<b>by </b><i><a class="txt" href="geomtrap.html#E4:66"><i><font color="Green" title="E65">A4</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</a></i>;<br/>
<b>hence </b><a NAME="E2:66_1"/>
<font color="Maroon" title="c10">t1</font>,<font color="Maroon" title="c11">t2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c12">w1</font>,<font color="Maroon" title="c13">w2</font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:66"><i><font color="Green" title="E62">A1</font></i></a>, <a class="txt" href="geomtrap.html#E2:66"><i><font color="Green" title="E63">A2</font></i></a>, <a class="txt" href="geomtrap.html#E3:66"><i><font color="Green" title="E64">A3</font></i></a>, <a class="ref" href="geomtrap.html#T39" target="_self" title="GEOMTRAP:th.39">Th39</a></i>;<br/>


</div><b>end;</b></div>
<b>set </b><font color="Maroon" title="c14">uu</font> = <font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">u2</font>;<br/>
<b>set </b><font color="Maroon" title="c15">vv</font> = <font color="Maroon" title="c8">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c9">v2</font>;<br/>
<a NAME="E6:66"/><i><font color="Green" title="E67">A6</font></i>: 
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">u2</font>,<font color="Maroon" title="c10">t1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c11">t2</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> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c8">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c12">w1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c13">w2</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="txt" href="geomtrap.html#E1:66"><i><font color="Green" title="E62">A1</font></i></a>, <a class="txt" href="geomtrap.html#E2:66"><i><font color="Green" title="E63">A2</font></i></a>, <a class="txt" href="geomtrap.html#E3:66"><i><font color="Green" title="E64">A3</font></i></a>, <a class="ref" href="geomtrap.html#T41" target="_self" title="GEOMTRAP:th.41">Th41</a></i>;<br/>
<a NAME="E7:66"/>
<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">u2</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">u2</font>,<font color="Maroon" title="c8">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c9">v2</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#E4:66"><i><font color="Green" title="E65">A4</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</a></i>;<br/>
<a NAME="E8:66"/><b>then </b><i><font color="Green" title="E68">A7</font></i>: 
<font color="Maroon" title="c10">t1</font>,<font color="Maroon" title="c11">t2</font>,<font color="Maroon" title="c10">t1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c11">t2</font>,<font color="Maroon" title="c12">w1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c13">w2</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#E1:66"><i><font color="Green" title="E62">A1</font></i></a>, <a class="txt" href="geomtrap.html#E2:66"><i><font color="Green" title="E63">A2</font></i></a>, <a class="txt" href="geomtrap.html#E3:66"><i><font color="Green" title="E64">A3</font></i></a>, <a class="txt" href="geomtrap.html#E6:66"><i><font color="Green" title="E67">A6</font></i></a>, <a class="ref" href="geomtrap.html#T42" target="_self" title="GEOMTRAP:th.42">Th42</a></i>;<br/>
<a NAME="E9:66"/>
<font color="Maroon" title="c8">v1</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">u2</font>,<font color="Maroon" title="c8">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c9">v2</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#E4:66"><i><font color="Green" title="E65">A4</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</a></i>;<br/>
<a NAME="E10:66"/><b>then </b>
<font color="Maroon" title="c12">w1</font>,<font color="Maroon" title="c13">w2</font>,<font color="Maroon" title="c10">t1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c11">t2</font>,<font color="Maroon" title="c12">w1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c13">w2</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#E1:66"><i><font color="Green" title="E62">A1</font></i></a>, <a class="txt" href="geomtrap.html#E2:66"><i><font color="Green" title="E63">A2</font></i></a>, <a class="txt" href="geomtrap.html#E3:66"><i><font color="Green" title="E64">A3</font></i></a>, <a class="txt" href="geomtrap.html#E6:66"><i><font color="Green" title="E67">A6</font></i></a>, <a class="ref" href="geomtrap.html#T42" target="_self" title="GEOMTRAP:th.42">Th42</a></i>;<br/>
<b>hence </b><a NAME="E11:66"/>
<font color="Maroon" title="c10">t1</font>,<font color="Maroon" title="c11">t2</font>,<font color="Maroon" title="c12">w1</font>,<font color="Maroon" title="c13">w2</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="txt" href="geomtrap.html#E5:66"><i><font color="Green" title="E66">A5</font></i></a>, <a class="txt" href="geomtrap.html#E8:66"><i><font color="Green" title="E68">A7</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</a></i>;<br/>


</div>
