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<b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">n</font> be   <a href="real_1.html#NM1">Real</a>;<br/>









<b>assume </b><a NAME="E1:11"/><i><font color="Green">E39</font></i>: 
 <a href="analmetr.html#R1">Gen</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 ;<br/>

<b>thus </b> <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K2">pr1</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="analort.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K3">pr2</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<span class="p4">(<span class="default"><font color="Maroon">n</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K2">pr1</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="analort.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="geomtrap.html#K3">pr2</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K2">pr1</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="analort.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K3">pr2</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T38">RLVECT_1:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K2">pr1</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="analort.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="geomtrap.html#K3">pr2</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T39">RLVECT_1:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K2">pr1</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="analort.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="rlvect_1.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="geomtrap.html#K3">pr2</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K2">pr1</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="analort.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="geomtrap.html#K3">pr2</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T39">RLVECT_1:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="geomtrap.html#K2">pr1</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="analort.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="geomtrap.html#K3">pr2</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<font color="Maroon">n</font> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="geomtrap.html#K2">pr1</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="analort.html#K1" target="_self">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="geomtrap.html#K3">pr2</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<font color="Maroon">n</font> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="geomtrap.html#K2">pr1</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="analort.html#K1" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="geomtrap.html#K3">pr2</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T39">RLVECT_1:39</a></i>
<br/>.= 
<font color="Maroon">n</font> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T38">RLVECT_1:38</a></i>
;<br/>


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