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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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">v</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="b5">a</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> holds <br/> (  <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="p1">(<span class="default"><font color="Olive" title="b5">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b3">u</font></span>)</span>,<font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a</font> <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="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font></span>)</span> &amp;  <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>,<font color="Olive" title="b3">u</font>,<span class="p1">(<span class="default"><font color="Olive" title="b5">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b4">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a</font> <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="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font></span>)</span> &amp;  <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="p1">(<span class="default"><font color="Olive" title="b5">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b3">u</font></span>)</span>,<font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<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>,<font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b5">a</font> &amp;  <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>,<font color="Olive" title="b3">u</font>,<span class="p1">(<span class="default"><font color="Olive" title="b5">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b4">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<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>,<font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b5">a</font> )</span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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">v</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="b3">a</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> holds <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="Olive" title="b3">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b1">u</font></span>)</span>,<font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a</font> <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>,<font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font></span>)</span> &amp;  <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>,<font color="Olive" title="b1">u</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a</font> <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>,<font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font></span>)</span> &amp;  <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="Olive" title="b3">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b1">u</font></span>)</span>,<font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b3">a</font> &amp;  <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>,<font color="Olive" title="b1">u</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b3">a</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:58"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
 <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</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="b3">a</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> holds <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="Olive" title="b3">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b1">u</font></span>)</span>,<font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a</font> <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>,<font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font></span>)</span> &amp;  <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>,<font color="Olive" title="b1">u</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a</font> <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>,<font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font></span>)</span> &amp;  <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="Olive" title="b3">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b1">u</font></span>)</span>,<font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b3">a</font> &amp;  <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>,<font color="Olive" title="b1">u</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b3">a</font> )</span><br/>

<div><span class="lab"><font color="Green" title="E54">A2</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> holds   <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="Olive" title="b1">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">u</font></span>)</span>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">a</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <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="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">u</font></span>)</span>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a</font> <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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></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="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">u</font></span>)</span>,<font color="Maroon" title="c5">v</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K2" title="GEOMTRAP:func.2">pr1</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<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">w</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font></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">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</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">w</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="geomtrap.html#E52"><span class="lab"><font color="Green" title="E47">Lm17</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K2" title="GEOMTRAP:func.2">pr1</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<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">w</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font></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"><font color="Maroon" title="c6">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<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">w</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="geomtrap.html#E52"><span class="lab"><font color="Green" title="E47">Lm17</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c6">a</font> <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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span>

;<br/><span class="kw">hence </span><a NAME="E2:58_1"/>
 <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="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">u</font></span>)</span>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a</font> <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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> holds <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="Olive" title="b1">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">u</font></span>)</span>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span> &amp;  <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>,<font color="Maroon" title="c4">u</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span> &amp;  <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="Olive" title="b1">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">u</font></span>)</span>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b1">a</font> &amp;  <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>,<font color="Maroon" title="c4">u</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b1">a</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">a</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <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="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">u</font></span>)</span>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a</font> <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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span> &amp;  <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>,<font color="Maroon" title="c4">u</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a</font> <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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span> &amp;  <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="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">u</font></span>)</span>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">a</font> &amp;  <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>,<font color="Maroon" title="c4">u</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">a</font> )</span><br/>



<span class="kw">thus </span><a NAME="E3:58"/>
 <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="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">u</font></span>)</span>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a</font> <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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58"><span class="lab"><font color="Green" title="E54">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <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>,<font color="Maroon" title="c4">u</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a</font> <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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span> &amp;  <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="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">u</font></span>)</span>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">a</font> &amp;  <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>,<font color="Maroon" title="c4">u</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">a</font> )</span><br/>

<span class="kw">thus </span> <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>,<font color="Maroon" title="c4">u</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font></span>)</span> = 
 <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="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font></span>)</span>,<font color="Maroon" title="c4">u</font>

<br/>.= 
<font color="Maroon" title="c6">a</font> <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>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58"><span class="lab"><font color="Green" title="E54">A2</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c6">a</font> <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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span>

; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <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="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">u</font></span>)</span>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">a</font> &amp;  <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>,<font color="Maroon" title="c4">u</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">a</font> )</span><br/>

<span class="kw">thus </span><a NAME="E5:58"/>
 <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="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">u</font></span>)</span>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58"><span class="lab"><font color="Green" title="E54">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <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>,<font color="Maroon" title="c4">u</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">a</font></span><br/>

<span class="kw">thus </span> <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>,<font color="Maroon" title="c4">u</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font></span>)</span> = 
 <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="c6">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font></span>)</span>,<font color="Maroon" title="c4">u</font>

<br/>.= 
<font color="Maroon" title="c6">a</font> <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>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58"><span class="lab"><font color="Green" title="E54">A2</font></span></a></span>
<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>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">a</font>

; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
