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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> 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/> <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>,<span class="p1">(<span class="default"><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></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b3">u</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> 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  <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"><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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">u</font> )</span><br/>







<b>assume </b><a NAME="E1:24"/><i><font color="Green" title="E21">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">  <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"><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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">u</font></span><br/>

<b>hence </b> <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"><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 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>,<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"><span class="p5">(<span class="default"><span class="p0">(<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>,<font color="Maroon" title="c4">u</font></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="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<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>,<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="c3">y</font></span>)</span></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>
<b>by </b><i><a class="ref" href="geomtrap.html#D5" title="GEOMTRAP:def.5">GEOMTRAP:def 5</a></i>
<br/>.= 
<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>,<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#K3" title="GEOMTRAP:func.3">pr2</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> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:24"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="geomtrap.html#D4" title="GEOMTRAP:def.4">GEOMTRAP:def 4</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>,<font color="Maroon" title="c4">u</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c2">x</font></span>)</span></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#K3" title="GEOMTRAP:func.3">pr2</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> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</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/>.= 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><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>,<font color="Maroon" title="c4">u</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font></span>)</span></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#K3" title="GEOMTRAP:func.3">pr2</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> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></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="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><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>,<font color="Maroon" title="c4">u</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font></span>)</span></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="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</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="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">y</font></span>)</span></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/>.= 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><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>,<font color="Maroon" title="c4">u</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span> <a href="analort.html#K1" title="ANALORT: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"><span class="p3">(<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>,<font color="Maroon" title="c4">u</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</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/>.= 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><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>,<font color="Maroon" title="c4">u</font></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="p2">(<span class="default"><span class="p3">(<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>,<font color="Maroon" title="c4">u</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T45" title="RLVECT_1:th.45">RLVECT_1:45</a></i>
<br/>.= 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">u</font>
<b>by </b><i><a class="txt" href="#E1:24"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="analort.html#E5"><i><font color="Green" title="E5">Lm5</font></i></a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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