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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="firebrick">::  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>, <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/><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>, <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:()"><span class="comment"><font color="firebrick">::  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> <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/>

















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:36"/><span class="lab"><font color="Green" title="E34">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="E2:36"/><span class="lab"><font color="Green" title="E35">A2</font></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>
 <span class="kw">and </span><br/><a NAME="E3:36"/><span class="lab"><font color="Green" title="E36">A3</font></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>,<font color="Maroon" title="c6">u1</font>
 <span class="kw">and </span><br/><a NAME="E4:36"/><span class="lab"><font color="Green" title="E37">A4</font></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>,<font color="Maroon" title="c7">v1</font>
 <span class="kw">and </span><br/><a NAME="E5:36"/><span class="lab"><font color="Green" title="E38">A5</font></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>,<font color="Maroon" title="c8">u2</font>
 <span class="kw">and </span><br/><a NAME="E6:36"/><span class="lab"><font color="Green" title="E39">A6</font></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>,<font color="Maroon" title="c9">v2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">reconsider </span><font color="Maroon" title="c10">p9</font> = <font color="Maroon" title="c4">u</font>, <font color="Maroon" title="c11">q9</font> = <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c12">p19</font> = <font color="Maroon" title="c6">u1</font>, <font color="Maroon" title="c13">q19</font> = <font color="Maroon" title="c7">v1</font>, <font color="Maroon" title="c14">p29</font> = <font color="Maroon" title="c8">u2</font>, <font color="Maroon" title="c15">q29</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> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T16" title="ANALMETR:th.16">ANALMETR:16</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c16">S9</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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="ref" href="geomtrap.html#T1" target="_self" title="GEOMTRAP:th.1">Th1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">S</font> =  <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c16">S9</font> as   <a href="diraf.html#NM1" title="DIRAF:NM.1">AffinSpace</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T41" title="DIRAF:th.41">DIRAF:41</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c18">p</font> = <font color="Maroon" title="c10">p9</font>, <font color="Maroon" title="c19">q</font> = <font color="Maroon" title="c11">q9</font>, <font color="Maroon" title="c20">p1</font> = <font color="Maroon" title="c12">p19</font>, <font color="Maroon" title="c21">q1</font> = <font color="Maroon" title="c13">q19</font>, <font color="Maroon" title="c22">p2</font> = <font color="Maroon" title="c14">p29</font>, <font color="Maroon" title="c23">q2</font> = <font color="Maroon" title="c15">q29</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="E11:36"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="ref" href="geomtrap.html#T3" target="_self" title="GEOMTRAP:th.3">Th3</a></span>;<br/>
<a NAME="E12:36"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A7</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E13:36"/>
<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="c21">q1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="txt" href="#E4:36"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="ref" href="geomtrap.html#T3" target="_self" title="GEOMTRAP:th.3">Th3</a></span>;<br/>
<a NAME="E14:36"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A8</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E15:36"/>
<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="c23">q2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="txt" href="#E6:36"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="ref" href="geomtrap.html#T3" target="_self" title="GEOMTRAP:th.3">Th3</a></span>;<br/>
<a NAME="E16:36"/><span class="kw">then </span>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E17:36"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A9</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="txt" href="#E12:36"><span class="lab"><font color="Green" title="E40">A7</font></span></a>, <a class="txt" href="#E14:36"><span class="lab"><font color="Green" title="E41">A8</font></span></a>, <a class="ref" href="aff_1.html#T8" title="AFF_1:th.8">AFF_1:8</a></span>;<br/>
<a NAME="E18:36"/>
<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="c22">p2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="txt" href="#E5:36"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="ref" href="geomtrap.html#T3" target="_self" title="GEOMTRAP:th.3">Th3</a></span>;<br/>
<a NAME="E19:36"/><span class="kw">then </span>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E20:36"/><span class="kw">then </span>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="txt" href="#E12:36"><span class="lab"><font color="Green" title="E40">A7</font></span></a>, <a class="txt" href="#E14:36"><span class="lab"><font color="Green" title="E41">A8</font></span></a>, <a class="ref" href="aff_1.html#T8" title="AFF_1:th.8">AFF_1:8</a></span>;<br/>
<a NAME="E21:36"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:36"><span class="lab"><font color="Green" title="E42">A9</font></span></a>, <a class="ref" href="aff_1.html#T10" title="AFF_1:th.10">AFF_1:10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E22:36"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="ref" href="geomtrap.html#T3" target="_self" title="GEOMTRAP:th.3">Th3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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