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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>, <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">v</font>, <font color="Olive" title="b5">u1</font>, <font color="Olive" title="b6">v1</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> &amp; <font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font>,<font color="Olive" title="b5">u1</font>,<font color="Olive" title="b6">v1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font> holds <br/><font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font>,<font color="Olive" title="b3">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Olive" title="b5">u1</font>,<font color="Olive" title="b4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Olive" title="b6">v1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font></span><br/><span class="kw">let </span><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>, <font color="Maroon" title="c6">u1</font>, <font color="Maroon" title="c7">v1</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> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> implies <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )</span><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:42"/><span class="lab"><font color="Green" title="E38">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>
 <span class="kw">and </span><br/><a NAME="E2:42"/><span class="lab"><font color="Green" title="E39">A2</font></span>: 
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</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"> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c8">p</font> = <font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">q</font> = <font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">r</font> = <font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">s</font> = <font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font>;<br/>
<a NAME="E3:42"/><span class="lab"><font color="Green" title="E40">A3</font></span>: 
( <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> &amp; <font color="Maroon" title="c6">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v1</font> implies <font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font></span>)</span> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="geomtrap.html#E27"><span class="lab"><font color="Green" title="E24">Lm9</font></span></a></span>;<br/>
<a NAME="E4:42"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="geomtrap.html#T8" target="_self" title="GEOMTRAP:th.8">Th8</a></span>;<br/>
<a NAME="E5:42"/><span class="kw">then </span>
<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="geomtrap.html#T14" target="_self" title="GEOMTRAP:th.14">Th14</a></span>;<br/>
<a NAME="E6:42"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A4</font></span>: 
<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="geomtrap.html#D1" target="_self" title="GEOMTRAP:def.1">Def1</a></span>;<br/>
<a NAME="E7:42"/>
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</a></span>;<br/>
<a NAME="E8:42"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A5</font></span>: 
( <font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font> implies ( <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font></span>)</span> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font></span>)</span> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="txt" href="geomtrap.html#E28"><span class="lab"><font color="Green" title="E25">Lm10</font></span></a></span>;<br/>
<div><span class="lab"><font color="Green" title="E43">A6</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:42_1"/>
<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</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="c6">u1</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font></span>)</span> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font></span>)</span> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )</span><br/><span class="kw">then </span><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="geomtrap.html#T8" target="_self" title="GEOMTRAP:th.8">Th8</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:42_1"/>
( <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font></span>)</span> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font></span>)</span> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="geomtrap.html#E27"><span class="lab"><font color="Green" title="E24">Lm9</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"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E10:42"/><span class="lab"><font color="Green" title="E44">A7</font></span>: 
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</a></span>;<br/>
<a NAME="E11:42"/><span class="kw">then </span>
<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">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/>
<a NAME="E12:42"/><span class="kw">then </span>
<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="geomtrap.html#T16" target="_self" title="GEOMTRAP:th.16">Th16</a></span>;<br/>
<a NAME="E13:42"/><span class="kw">then </span>
<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="geomtrap.html#D1" target="_self" title="GEOMTRAP:def.1">Def1</a></span>;<br/>
<a NAME="E14:42"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A8</font></span>: 
( <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> &amp; <font color="Maroon" title="c6">u1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">v1</font> implies <font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font></span>)</span> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E9:42"><span class="lab"><font color="Green" title="E43">A6</font></span></a>, <a class="txt" href="#E8:42"><span class="lab"><font color="Green" title="E42">A5</font></span></a>, <a class="txt" href="geomtrap.html#E28"><span class="lab"><font color="Green" title="E25">Lm10</font></span></a></span>;<br/>
<a NAME="E15:42"/><span class="lab"><font color="Green" title="E46">A9</font></span>: 
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:42"><span class="lab"><font color="Green" title="E44">A7</font></span></a>, <a class="ref" href="geomtrap.html#T16" target="_self" title="GEOMTRAP:th.16">Th16</a></span>;<br/>
<a NAME="E16:42"/><span class="kw">then </span>
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="geomtrap.html#D1" target="_self" title="GEOMTRAP:def.1">Def1</a></span>;<br/>
<a NAME="E17:42"/><span class="kw">then </span>
( <font color="Maroon" title="c4">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">v</font> implies <font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font></span>)</span> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E9:42"><span class="lab"><font color="Green" title="E43">A6</font></span></a>, <a class="txt" href="#E8:42"><span class="lab"><font color="Green" title="E42">A5</font></span></a>, <a class="txt" href="geomtrap.html#E28"><span class="lab"><font color="Green" title="E25">Lm10</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:42"/>
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:42"><span class="lab"><font color="Green" title="E46">A9</font></span></a>, <a class="txt" href="#E9:42"><span class="lab"><font color="Green" title="E43">A6</font></span></a>, <a class="txt" href="#E8:42"><span class="lab"><font color="Green" title="E42">A5</font></span></a>, <a class="txt" href="#E14:42"><span class="lab"><font color="Green" title="E45">A8</font></span></a>, <a class="txt" href="#E3:42"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</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>
