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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">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>, <font color="Olive" title="b7">u2</font>, <font color="Olive" title="b8">v2</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> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">v</font> &amp; <font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Olive" title="b3">u</font>,<font color="Olive" title="b5">u1</font> &amp; <font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Olive" title="b3">u</font>,<font color="Olive" title="b6">v1</font> &amp; <font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Olive" title="b3">u</font>,<font color="Olive" title="b7">u2</font> &amp; <font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Olive" title="b3">u</font>,<font color="Olive" title="b8">v2</font> holds <br/><font color="Olive" title="b5">u1</font>,<font color="Olive" title="b6">v1</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Olive" title="b7">u2</font>,<font color="Olive" title="b8">v2</font></span><br/><b>let </b><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>, <font color="Maroon" title="c8">u2</font>, <font color="Maroon" title="c9">v2</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> &amp; <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> &amp; <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>,<font color="Maroon" title="c6">u1</font> &amp; <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>,<font color="Maroon" title="c7">v1</font> &amp; <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>,<font color="Maroon" title="c8">u2</font> &amp; <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>,<font color="Maroon" title="c9">v2</font> implies <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="c8">u2</font>,<font color="Maroon" title="c9">v2</font> )</span><br/>

















<b>assume </b><b>that </b><br/><a NAME="E1:36"/><i><font color="Green" title="E34">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="E2:36"/><i><font color="Green" title="E35">A2</font></i>: 
<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>
 <b>and </b><br/><a NAME="E3:36"/><i><font color="Green" title="E36">A3</font></i>: 
( <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>,<font color="Maroon" title="c6">u1</font> &amp; <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>,<font color="Maroon" title="c7">v1</font> &amp; <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>,<font color="Maroon" title="c8">u2</font> &amp; <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>,<font color="Maroon" title="c9">v2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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="c8">u2</font>,<font color="Maroon" title="c9">v2</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c10">p'</font> = <font color="Maroon" title="c4">u</font>, <font color="Maroon" title="c11">q'</font> = <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c12">p1'</font> = <font color="Maroon" title="c6">u1</font>, <font color="Maroon" title="c13">q1'</font> = <font color="Maroon" title="c7">v1</font>, <font color="Maroon" title="c14">p2'</font> = <font color="Maroon" title="c8">u2</font>, <font color="Maroon" title="c15">q2'</font> = <font color="Maroon" title="c9">v2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <span class="p2">(<span class="default"><a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T22" title="ANALMETR:th.22">ANALMETR:22</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c16">S'</font> =  <a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <font color="Maroon" title="c1">V</font> as   <a href="analoaf.html#NM1" title="ANALOAF:NM.1">OAffinSpace</a> <b>by </b><i><a class="txt" href="geomtrap.html#E1:36"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="geomtrap.html#T1" target="_self" title="GEOMTRAP:th.1">Th1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c17">S</font> =  <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c16">S'</font> as   <a href="diraf.html#NM1" title="DIRAF:NM.1">AffinSpace</a> <b>by </b><i><a class="ref" href="diraf.html#T48" title="DIRAF:th.48">DIRAF:48</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c18">p</font> = <font color="Maroon" title="c10">p'</font>, <font color="Maroon" title="c19">q</font> = <font color="Maroon" title="c11">q'</font>, <font color="Maroon" title="c20">p1</font> = <font color="Maroon" title="c12">p1'</font>, <font color="Maroon" title="c21">q1</font> = <font color="Maroon" title="c13">q1'</font>, <font color="Maroon" title="c22">p2</font> = <font color="Maroon" title="c14">p2'</font>, <font color="Maroon" title="c23">q2</font> = <font color="Maroon" title="c15">q2'</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c17">S</font> ;<br/>
<a NAME="E8:36"/>
( <font color="Maroon" title="c18">p</font>,<font color="Maroon" title="c19">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p</font>,<font color="Maroon" title="c20">p1</font> &amp; <font color="Maroon" title="c18">p</font>,<font color="Maroon" title="c19">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p</font>,<font color="Maroon" title="c21">q1</font> &amp; <font color="Maroon" title="c18">p</font>,<font color="Maroon" title="c19">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p</font>,<font color="Maroon" title="c22">p2</font> &amp; <font color="Maroon" title="c18">p</font>,<font color="Maroon" title="c19">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">p</font>,<font color="Maroon" title="c23">q2</font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E1:36"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="geomtrap.html#E3:36"><i><font color="Green" title="E36">A3</font></i></a>, <a class="ref" href="geomtrap.html#T3" target="_self" title="GEOMTRAP:th.3">Th3</a></i>;<br/>
<a NAME="E9:36"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">p</font>,<font color="Maroon" title="c19">q</font>,<font color="Maroon" title="c20">p1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">p</font>,<font color="Maroon" title="c19">q</font>,<font color="Maroon" title="c21">q1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">p</font>,<font color="Maroon" title="c19">q</font>,<font color="Maroon" title="c22">p2</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">p</font>,<font color="Maroon" title="c19">q</font>,<font color="Maroon" title="c23">q2</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:36"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">p1</font>,<font color="Maroon" title="c21">q1</font>,<font color="Maroon" title="c22">p2</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">p1</font>,<font color="Maroon" title="c21">q1</font>,<font color="Maroon" title="c23">q2</font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E2:36"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></i>;<br/>
<a NAME="E11:36"/><b>then </b>
<font color="Maroon" title="c20">p1</font>,<font color="Maroon" title="c21">q1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">p2</font>,<font color="Maroon" title="c23">q2</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T19" title="AFF_1:th.19">AFF_1:19</a></i>;<br/>
<b>hence </b><a NAME="E12:36"/>
<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="c8">u2</font>,<font color="Maroon" title="c9">v2</font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:36"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="geomtrap.html#T3" target="_self" title="GEOMTRAP:th.3">Th3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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