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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">u</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">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 <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">v</font> holds <br/><font color="Olive" title="b1">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Olive" title="b2">y</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Olive" title="b2">y</font>,<font color="Olive" title="b2">y</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Olive" title="b3">v</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">u</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">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"> ( <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font> implies <font color="Maroon" title="c2">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">v</font> )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">p</font> = <font color="Maroon" title="c2">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c3">y</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">q</font> = <font color="Maroon" title="c3">y</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">v</font>;<br/>
<a NAME="E1:18"/>
<font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c2">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="geomtrap.html#T13" target="_self" title="GEOMTRAP:th.13">Th13</a></span>;<br/>
<a NAME="E2:18"/><span class="kw">then </span>
<font color="Maroon" title="c2">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="geomtrap.html#E17"><span class="lab"><font color="Green" title="E14">Lm1</font></span></a></span>;<br/>
<a NAME="E3:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</a></span>;<br/>
<a NAME="E4:18"/>
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c3">y</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="geomtrap.html#T13" target="_self" title="GEOMTRAP:th.13">Th13</a></span>;<br/>
<a NAME="E5:18"/><span class="kw">then </span>
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="geomtrap.html#E17"><span class="lab"><font color="Green" title="E14">Lm1</font></span></a></span>;<br/>
<a NAME="E6:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A2</font></span>: 
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</a></span>;<br/>
<span class="kw">assume </span><a NAME="E7:18"/><span class="lab"><font color="Green" title="E18">A3</font></span>: 
<font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">v</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:18_1"/><span class="lab"><font color="Green" title="E19">A4</font></span>: 
<font color="Maroon" title="c2">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">y</font>
 <span class="kw">and </span><br/><a NAME="E2:18_1"/><span class="lab"><font color="Green" title="E20">A5</font></span>: 
<font color="Maroon" title="c3">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">v</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">v</font></span><br/><a NAME="E3:18_1"/>
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E1:18_1"><span class="lab"><font color="Green" title="E19">A4</font></span></a>, <a class="ref" href="analoaf.html#T20" title="ANALOAF:th.20">ANALOAF:20</a></span>;<br/><span class="kw">hence </span><a NAME="E4:18_1"/>
<font color="Maroon" title="c2">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E2:18_1"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="ref" href="analoaf.html#T20" title="ANALOAF:th.20">ANALOAF:20</a></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">hence </span><a NAME="E9:18"/>
<font color="Maroon" title="c2">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c3">y</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">v</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#T18" title="ANALOAF:th.18">ANALOAF:18</a></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/>


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