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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">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">v</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">x</font>,<font color="Olive" title="b2">y</font> holds <br/><font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">u</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b4">v</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">u</font>, <font color="Maroon" title="c5">v</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> implies <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )</span><br/>









<b>assume </b><a NAME="E1:35"/><i><font color="Green" title="E30">A1</font></i>: 
 <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span><br/>

<b>set </b><font color="Maroon" title="c6">w</font> = <span class="p1">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font></span>)</span>;<br/>
<i><font color="Green" title="E31">A2</font></i>: <span class="p1">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font></span>)</span> = 
 <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:35"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="analort.html#T11" target="_self" title="ANALORT:th.11">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="analort.html#K1" title="ANALORT:func.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> <span class="p3">(<span class="default"><a href="geomtrap.html#K2" title="GEOMTRAP:func.2">pr1</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span>

;<br/>
 <a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K2" title="GEOMTRAP:func.2">pr1</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K2" title="GEOMTRAP:func.2">pr1</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="geomtrap.html#D6" title="GEOMTRAP:def.6">GEOMTRAP:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K2" title="GEOMTRAP:func.2">pr1</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:35"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="#E2:35"><i><font color="Green" title="E31">A2</font></i></a>, <a class="txt" href="analort.html#E6"><i><font color="Green" title="E6">Lm6</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K2" title="GEOMTRAP:func.2">pr1</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</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> <span class="p3">(<span class="default"><a href="geomtrap.html#K2" title="GEOMTRAP:func.2">pr1</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:35"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="#E2:35"><i><font color="Green" title="E31">A2</font></i></a>, <a class="txt" href="analort.html#E6"><i><font color="Green" title="E6">Lm6</font></i></a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 

;<br/>
<a NAME="E4:35"/><b>then </b>
<font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font>,<span class="p1">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font></span>)</span> <a href="analmetr.html#R2" title="ANALMETR:pred.2">are_Ort_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 
<b>by </b><i><a class="txt" href="#E1:35"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="geomtrap.html#T34" title="GEOMTRAP:th.34">GEOMTRAP:34</a></i>;<br/>
<b>hence </b><a NAME="E5:35"/>
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font>, <a href="analort.html#K3" title="ANALORT:func.3">Orte</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D3" title="ANALMETR:def.3">ANALMETR:def 3</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>
