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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">u1</font>, <font color="Olive" title="b4">v1</font>, <font color="Olive" title="b5">u</font>, <font color="Olive" title="b6">v</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">u1</font>,<font color="Olive" title="b4">v1</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Olive" title="b5">u</font>,<font color="Olive" title="b6">v</font> or <font color="Olive" title="b5">u</font>,<font color="Olive" title="b6">v</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Olive" title="b3">u1</font>,<font color="Olive" title="b4">v1</font> ) &amp; ( <font color="Olive" title="b7">u2</font>,<font color="Olive" title="b8">v2</font>,<font color="Olive" title="b5">u</font>,<font color="Olive" title="b6">v</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font> or <font color="Olive" title="b5">u</font>,<font color="Olive" title="b6">v</font>,<font color="Olive" title="b7">u2</font>,<font color="Olive" title="b8">v2</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font> ) &amp; <font color="Olive" title="b5">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">v</font> holds <br/>( <font color="Olive" title="b3">u1</font>,<font color="Olive" title="b4">v1</font>,<font color="Olive" title="b7">u2</font>,<font color="Olive" title="b8">v2</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b7">u2</font>,<font color="Olive" title="b8">v2</font>,<font color="Olive" title="b3">u1</font>,<font color="Olive" title="b4">v1</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</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">u1</font>, <font color="Maroon" title="c5">v1</font>, <font color="Maroon" title="c6">u</font>, <font color="Maroon" title="c7">v</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">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">v</font> or <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">v</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> ) &amp; ( <font color="Maroon" title="c8">u2</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">v</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> or <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">v</font>,<font color="Maroon" title="c8">u2</font>,<font color="Maroon" title="c9">v2</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">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">v</font> implies ( <font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font>,<font color="Maroon" title="c8">u2</font>,<font color="Maroon" title="c9">v2</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="c8">u2</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">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><br/>

















<b>assume </b><b>that </b><br/><a NAME="E1:26"/><i><font color="Green" title="E26">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="E2:26"/><i><font color="Green" title="E27">A2</font></i>: 
( <font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">v</font> or <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">v</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> )
 <b>and </b><br/><a NAME="E3:26"/><i><font color="Green" title="E28">A3</font></i>: 
( <font color="Maroon" title="c8">u2</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">v</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> or <font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c7">v</font>,<font color="Maroon" title="c8">u2</font>,<font color="Maroon" title="c9">v2</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> )
 <b>and </b><br/><a NAME="E4:26"/><i><font color="Green" title="E29">A4</font></i>: 
<font color="Maroon" title="c6">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">v</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font>,<font color="Maroon" title="c8">u2</font>,<font color="Maroon" title="c9">v2</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="c8">u2</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">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><br/>

<b>reconsider </b><font color="Maroon" title="c10">S</font> =  <a href="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> as   <a href="analmetr.html#NM1" title="ANALMETR:NM.1">OrtAfSp</a> <b>by </b><i><a class="txt" href="geomtrap.html#E1:26"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="analmetr.html#T44" title="ANALMETR:th.44">ANALMETR:44</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">p'</font> = <font color="Maroon" title="c6">u</font>, <font color="Maroon" title="c12">q'</font> = <font color="Maroon" title="c7">v</font>, <font color="Maroon" title="c13">p1'</font> = <font color="Maroon" title="c4">u1</font>, <font color="Maroon" title="c14">q1'</font> = <font color="Maroon" title="c5">v1</font>, <font color="Maroon" title="c15">p2'</font> = <font color="Maroon" title="c8">u2</font>, <font color="Maroon" title="c16">q2'</font> = <font color="Maroon" title="c9">v2</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 <span class="p1">(<span class="default"><a href="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T28" title="ANALMETR:th.28">ANALMETR:28</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c17">p</font> = <font color="Maroon" title="c11">p'</font>, <font color="Maroon" title="c18">q</font> = <font color="Maroon" title="c12">q'</font>, <font color="Maroon" title="c19">p1</font> = <font color="Maroon" title="c13">p1'</font>, <font color="Maroon" title="c20">q1</font> = <font color="Maroon" title="c14">q1'</font>, <font color="Maroon" title="c21">p2</font> = <font color="Maroon" title="c15">p2'</font>, <font color="Maroon" title="c22">q2</font> = <font color="Maroon" title="c16">q2'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c10">S</font> ;<br/>
<a NAME="E8:26"/><i><font color="Green" title="E30">A5</font></i>: 
( <font color="Maroon" title="c21">p2</font>,<font color="Maroon" title="c22">q2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c17">p</font>,<font color="Maroon" title="c18">q</font> or <font color="Maroon" title="c17">p</font>,<font color="Maroon" title="c18">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c21">p2</font>,<font color="Maroon" title="c22">q2</font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E3:26"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="analmetr.html#T31" title="ANALMETR:th.31">ANALMETR:31</a></i>;<br/>
<a NAME="E9:26"/>
( <font color="Maroon" title="c19">p1</font>,<font color="Maroon" title="c20">q1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">p</font>,<font color="Maroon" title="c18">q</font> or <font color="Maroon" title="c17">p</font>,<font color="Maroon" title="c18">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">p1</font>,<font color="Maroon" title="c20">q1</font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E2:26"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="geomtrap.html#T4" target="_self" title="GEOMTRAP:th.4">Th4</a></i>;<br/>
<a NAME="E10:26"/><b>then </b>
( <font color="Maroon" title="c19">p1</font>,<font color="Maroon" title="c20">q1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c21">p2</font>,<font color="Maroon" title="c22">q2</font> &amp; <font color="Maroon" title="c21">p2</font>,<font color="Maroon" title="c22">q2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c19">p1</font>,<font color="Maroon" title="c20">q1</font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E4:26"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="geomtrap.html#E8:26"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E11:26"/>
( <font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font>,<font color="Maroon" title="c8">u2</font>,<font color="Maroon" title="c9">v2</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="c8">u2</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">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> )
 <b>by </b><i><a class="ref" href="analmetr.html#T31" title="ANALMETR:th.31">ANALMETR:31</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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