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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> 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> holds <br/>for <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">u'</font>, <font color="Olive" title="b5">u1</font>, <font color="Olive" title="b6">u2</font>, <font color="Olive" title="b7">t1</font>, <font color="Olive" title="b8">t2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><br/> for <font color="Olive" title="b9">A1</font>, <font color="Olive" title="b10">A2</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b3">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">u'</font> &amp; <font color="Olive" title="b9">A1</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="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b4">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b4">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font>,<span class="p4">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b4">u'</font></span>)</span>,<font color="Olive" title="b5">u1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b4">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b4">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> &amp; <font color="Olive" title="b10">A2</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="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b4">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b4">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font>,<span class="p4">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b4">u'</font></span>)</span>,<font color="Olive" title="b6">u2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b4">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b4">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> &amp; <font color="Olive" title="b7">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">u1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b9">A1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b4">u'</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b8">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">u2</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b10">A2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b4">u'</font></span>)</span></span>)</span> holds <br/>( <font color="Olive" title="b8">t2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b7">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b5">u1</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="Olive" title="b10">A2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Olive" title="b9">A1</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b4">u'</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b10">A2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Olive" title="b9">A1</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="real_1.html#K1" title="REAL_1:func.1">-</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b4">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b6">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b5">u1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b4">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b4">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> )</span><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>; <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> implies for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">u'</font>, <font color="Olive" title="b3">u1</font>, <font color="Olive" title="b4">u2</font>, <font color="Olive" title="b5">t1</font>, <font color="Olive" title="b6">t2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><br/> for <font color="Olive" title="b7">A1</font>, <font color="Olive" title="b8">A2</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">u'</font> &amp; <font color="Olive" title="b7">A1</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="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span>,<font color="Olive" title="b3">u1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> &amp; <font color="Olive" title="b8">A2</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="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span>,<font color="Olive" title="b4">u2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> &amp; <font color="Olive" title="b5">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">u1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">A1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b6">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">u2</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b8">A2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span></span>)</span> holds <br/>( <font color="Olive" title="b6">t2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b5">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b3">u1</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="Olive" title="b8">A2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Olive" title="b7">A1</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b8">A2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Olive" title="b7">A1</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="real_1.html#K1" title="REAL_1:func.1">-</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b4">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b3">u1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> ) )</span><br/>





<b>assume </b><a NAME="E1:62"/><i><font color="Green" title="E59">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>
 ; <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">u</font>, <font color="Olive" title="b2">u'</font>, <font color="Olive" title="b3">u1</font>, <font color="Olive" title="b4">u2</font>, <font color="Olive" title="b5">t1</font>, <font color="Olive" title="b6">t2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><br/> for <font color="Olive" title="b7">A1</font>, <font color="Olive" title="b8">A2</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">u'</font> &amp; <font color="Olive" title="b7">A1</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="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span>,<font color="Olive" title="b3">u1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> &amp; <font color="Olive" title="b8">A2</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="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span>,<font color="Olive" title="b4">u2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> &amp; <font color="Olive" title="b5">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">u1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">A1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b6">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">u2</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b8">A2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span></span>)</span> holds <br/>( <font color="Olive" title="b6">t2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b5">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b3">u1</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="Olive" title="b8">A2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Olive" title="b7">A1</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b8">A2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Olive" title="b7">A1</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="real_1.html#K1" title="REAL_1:func.1">-</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b4">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b3">u1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> )</span><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">t1</font>, <font color="Maroon" title="c9">t2</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"> for <font color="Olive" title="b1">A1</font>, <font color="Olive" title="b2">A2</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <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> &amp; <font color="Olive" title="b1">A1</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="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<font color="Maroon" title="c6">u1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> &amp; <font color="Olive" title="b2">A2</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="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<font color="Maroon" title="c7">u2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> &amp; <font color="Maroon" title="c8">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">A1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c9">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">A2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> holds <br/>( <font color="Maroon" title="c9">t2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c8">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</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="Olive" title="b2">A2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Olive" title="b1">A1</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b2">A2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Olive" title="b1">A1</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="real_1.html#K1" title="REAL_1:func.1">-</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> )</span><br/><b>let </b><font color="Maroon" title="c10">A1</font>, <font color="Maroon" title="c11">A2</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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> &amp; <font color="Maroon" title="c10">A1</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="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<font color="Maroon" title="c6">u1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> &amp; <font color="Maroon" title="c11">A2</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="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<font color="Maroon" title="c7">u2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> &amp; <font color="Maroon" title="c8">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">A1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c9">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">A2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> implies ( <font color="Maroon" title="c9">t2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c8">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</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="c11">A2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c10">A1</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c11">A2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c10">A1</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="real_1.html#K1" title="REAL_1:func.1">-</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> ) )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E2:62"/>
<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="E3:62"/><i><font color="Green" title="E60">A2</font></i>: 
<font color="Maroon" title="c10">A1</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="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<font color="Maroon" title="c6">u1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span>
 <b>and </b><br/><a NAME="E4:62"/><i><font color="Green" title="E61">A3</font></i>: 
<font color="Maroon" title="c11">A2</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="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<font color="Maroon" title="c7">u2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span>
 <b>and </b><br/><a NAME="E5:62"/><i><font color="Green" title="E62">A4</font></i>: 
( <font color="Maroon" title="c8">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">A1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c9">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">A2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c9">t2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c8">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</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="c11">A2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c10">A1</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c11">A2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c10">A1</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="real_1.html#K1" title="REAL_1:func.1">-</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> )</span><br/>

<b>thus </b><a NAME="E6:62"/>
( <font color="Maroon" title="c9">t2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c8">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</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="c11">A2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c10">A1</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c11">A2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c10">A1</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="real_1.html#K1" title="REAL_1:func.1">-</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c12">uu</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<font color="Maroon" title="c7">u2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<font color="Maroon" title="c6">u1</font></span>)</span></span>)</span></span>)</span>;<br/>
<a NAME="E1:62_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<font color="Maroon" title="c7">u2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<font color="Maroon" title="c6">u1</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_1"><b>proof </b></a><div class="add">

<i><font color="Green" title="E63">A5</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<font color="Maroon" title="c7">u2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<font color="Maroon" title="c6">u1</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c7">u2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<font color="Maroon" title="c6">u1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:62"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="geomtrap.html#T33" target="_self" title="GEOMTRAP:th.33">Th33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c7">u2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:62"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="geomtrap.html#T33" target="_self" title="GEOMTRAP:th.33">Th33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u1</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c7">u2</font></span>)</span></span>)</span>

<br/>.= 
 <a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c7">u2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:62"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="geomtrap.html#T32" target="_self" title="GEOMTRAP:th.32">Th32</a></i>
;<br/>
<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c7">u2</font></span>)</span> = 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c7">u2</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T47" title="RLVECT_1:th.47">RLVECT_1:47</a></i>
<br/>.= 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T48" title="RLVECT_1:th.48">RLVECT_1:48</a></i>
<br/>.= 
2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</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="c7">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T39" title="RLVECT_1:th.39">RLVECT_1:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 2</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T38" title="RLVECT_1:th.38">RLVECT_1:38</a></i>
;<br/>
<b>hence </b><a NAME="E3:62_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<font color="Maroon" title="c7">u2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<font color="Maroon" title="c6">u1</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:62"><i><font color="Green" title="E59">A1</font></i></a>, <a class="txt" href="#E1:62_1_1"><i><font color="Green" title="E63">A5</font></i></a>, <a class="ref" href="geomtrap.html#T33" target="_self" title="GEOMTRAP:th.33">Th33</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>
<b>hence </b><a NAME="E2:62_1"/>
( <font color="Maroon" title="c9">t2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c8">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</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="c11">A2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c10">A1</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c11">A2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c10">A1</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="real_1.html#K1" title="REAL_1:func.1">-</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c7">u2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">u'</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="#E3:62"><i><font color="Green" title="E60">A2</font></i></a>, <a class="txt" href="#E4:62"><i><font color="Green" title="E61">A3</font></i></a>, <a class="txt" href="#E5:62"><i><font color="Green" title="E62">A4</font></i></a>, <a class="txt" href="geomtrap.html#E55"><i><font color="Green" title="E50">Lm19</font></i></a>, <a class="ref" href="xcmplx_1.html#T40" title="XCMPLX_1:th.40">XCMPLX_1:40</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>


</div>
