<?xml version="1.0"?>
<div class="add">

<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">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><br/> for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font>, <font color="Olive" title="b5">a</font>, <font color="Olive" title="b6">a1</font>, <font color="Olive" title="b7">b</font>, <font color="Olive" title="b8">b1</font>, <font color="Olive" title="b9">c</font>, <font color="Olive" title="b10">c1</font>, <font color="Olive" title="b11">d</font>, <font color="Olive" title="b12">d1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K7" title="GEOMTRAP:func.7">DTrSpace</a> <font color="Maroon" title="c1">V</font>,<font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font></span>)</span>  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">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">q</font> &amp; <font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">a</font>,<font color="Olive" title="b6">a1</font> &amp; <font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b7">b</font>,<font color="Olive" title="b8">b1</font> &amp; <font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b9">c</font>,<font color="Olive" title="b10">c1</font> &amp; <font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b11">d</font>,<font color="Olive" title="b12">d1</font> &amp; <font color="Olive" title="b5">a</font>,<font color="Olive" title="b7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b9">c</font>,<font color="Olive" title="b11">d</font> holds <br/><font color="Olive" title="b6">a1</font>,<font color="Olive" title="b8">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b10">c1</font>,<font color="Olive" title="b12">d1</font></span><br/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">a1</font>, <font color="Olive" title="b5">b</font>, <font color="Olive" title="b6">b1</font>, <font color="Olive" title="b7">c</font>, <font color="Olive" title="b8">c1</font>, <font color="Olive" title="b9">d</font>, <font color="Olive" title="b10">d1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K7" title="GEOMTRAP:func.7">DTrSpace</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font></span>)</span>  st  <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="Olive" title="b1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">q</font> &amp; <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">a1</font> &amp; <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b</font>,<font color="Olive" title="b6">b1</font> &amp; <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b7">c</font>,<font color="Olive" title="b8">c1</font> &amp; <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b9">d</font>,<font color="Olive" title="b10">d1</font> &amp; <font color="Olive" title="b3">a</font>,<font color="Olive" title="b5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b7">c</font>,<font color="Olive" title="b9">d</font> holds <br/><font color="Olive" title="b4">a1</font>,<font color="Olive" title="b6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b8">c1</font>,<font color="Olive" title="b10">d1</font></span><br/><b>let </b><font color="Maroon" title="c4">p</font>, <font color="Maroon" title="c5">q</font>, <font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">a1</font>, <font color="Maroon" title="c8">b</font>, <font color="Maroon" title="c9">b1</font>, <font color="Maroon" title="c10">c</font>, <font color="Maroon" title="c11">c1</font>, <font color="Maroon" title="c12">d</font>, <font color="Maroon" title="c13">d1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K7" title="GEOMTRAP:func.7">DTrSpace</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font></span>)</span>; <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">w</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">q</font> &amp; <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">a1</font> &amp; <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c9">b1</font> &amp; <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c11">c1</font> &amp; <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c13">d1</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c12">d</font> implies <font color="Maroon" title="c7">a1</font>,<font color="Maroon" title="c9">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c13">d1</font> )</span><br/>

























<b>assume </b><b>that </b><br/><a NAME="E1:92"/><i><font color="Green" title="E81">A1</font></i>: 
 <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>
 <b>and </b><br/><a NAME="E2:92"/><i><font color="Green" title="E82">Y</font></i>: 
<font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">q</font>
 <b>and </b><br/><a NAME="E3:92"/><i><font color="Green" title="E83">X</font></i>: 
( <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">a1</font> &amp; <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c9">b1</font> &amp; <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c11">c1</font> &amp; <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c13">d1</font> )
 <b>and </b><br/><a NAME="E4:92"/><i><font color="Green" title="E84">A2</font></i>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c12">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">a1</font>,<font color="Maroon" title="c9">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c13">d1</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c14">u</font> = <font color="Maroon" title="c4">p</font>, <font color="Maroon" title="c15">u'</font> = <font color="Maroon" title="c5">q</font>, <font color="Maroon" title="c16">u1</font> = <font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c17">u2</font> = <font color="Maroon" title="c8">b</font>, <font color="Maroon" title="c18">v1</font> = <font color="Maroon" title="c10">c</font>, <font color="Maroon" title="c19">v2</font> = <font color="Maroon" title="c12">d</font>, <font color="Maroon" title="c20">t1</font> = <font color="Maroon" title="c7">a1</font>, <font color="Maroon" title="c21">t2</font> = <font color="Maroon" title="c9">b1</font>, <font color="Maroon" title="c22">w1</font> = <font color="Maroon" title="c11">c1</font>, <font color="Maroon" title="c23">w2</font> = <font color="Maroon" title="c13">d1</font> as   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> ;<br/>
<a NAME="E6:92"/>
( <font color="Maroon" title="c14">u</font>,<font color="Maroon" title="c15">u'</font>,<font color="Maroon" title="c16">u1</font>,<font color="Maroon" title="c20">t1</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> &amp; <font color="Maroon" title="c14">u</font>,<font color="Maroon" title="c15">u'</font>,<font color="Maroon" title="c17">u2</font>,<font color="Maroon" title="c21">t2</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> &amp; <font color="Maroon" title="c14">u</font>,<font color="Maroon" title="c15">u'</font>,<font color="Maroon" title="c18">v1</font>,<font color="Maroon" title="c22">w1</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> &amp; <font color="Maroon" title="c14">u</font>,<font color="Maroon" title="c15">u'</font>,<font color="Maroon" title="c19">v2</font>,<font color="Maroon" title="c23">w2</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> &amp; <font color="Maroon" title="c16">u1</font>,<font color="Maroon" title="c17">u2</font>,<font color="Maroon" title="c18">v1</font>,<font color="Maroon" title="c19">v2</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> )
 
<b>by </b><i><a class="txt" href="#E1:92"><i><font color="Green" title="E81">A1</font></i></a>, <a class="txt" href="#E4:92"><i><font color="Green" title="E84">A2</font></i></a>, <a class="ref" href="geomtrap.html#T47" target="_self" title="GEOMTRAP:th.47">Th47</a>, <a class="txt" href="#E3:92"><i><font color="Green" title="E83">X</font></i></a></i>;<br/>
<a NAME="E7:92"/><b>then </b>
<font color="Maroon" title="c20">t1</font>,<font color="Maroon" title="c21">t2</font>,<font color="Maroon" title="c22">w1</font>,<font color="Maroon" title="c23">w2</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>
 
<b>by </b><i><a class="txt" href="#E1:92"><i><font color="Green" title="E81">A1</font></i></a>, <a class="ref" href="geomtrap.html#T43" target="_self" title="GEOMTRAP:th.43">Th43</a>, <a class="txt" href="#E2:92"><i><font color="Green" title="E82">Y</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:92"/>
<font color="Maroon" title="c7">a1</font>,<font color="Maroon" title="c9">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c13">d1</font>
 <b>by </b><i><a class="txt" href="#E1:92"><i><font color="Green" title="E81">A1</font></i></a>, <a class="ref" href="geomtrap.html#T47" target="_self" title="GEOMTRAP:th.47">Th47</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
