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<b>consider </b><font color="Maroon" title="c1">V</font> being   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>, <font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E2:5_1_1"/><i><font color="Green" title="E4">A1</font></i>: 
 <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T7" title="ANALMETR:th.7">ANALMETR:7</a></i>;<br/>
<b>take </b><font color="Maroon" title="c4">C</font> =  <a href="analort.html#K6" title="ANALORT:func.6">CESpace</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</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">C</font> is <a href="dirort.html#V1" title="DIRORT:attr.1">Oriented_Orthogonality_Space-like</a></span><br/>

<b>thus </b><a NAME="E3:5_1_1"/>
( ( for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">u1</font>, <font color="Olive" title="b3">v</font>, <font color="Olive" title="b4">v1</font>, <font color="Olive" title="b5">w</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">C</font> holds <br/> ( <font color="Olive" title="b1">u</font>,<font color="Olive" title="b1">u</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b3">v</font>,<font color="Olive" title="b5">w</font> &amp; <font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">v</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b5">w</font>,<font color="Olive" title="b5">w</font> &amp; ( <font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">v</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b2">u1</font>,<font color="Olive" title="b4">v1</font> &amp; <font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">v</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b4">v1</font>,<font color="Olive" title="b2">u1</font> &amp; not <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v</font> implies <font color="Olive" title="b2">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">v1</font> ) &amp; ( <font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">v</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b2">u1</font>,<font color="Olive" title="b4">v1</font> &amp; <font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">v</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b2">u1</font>,<font color="Olive" title="b5">w</font> &amp; not <font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">v</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b4">v1</font>,<font color="Olive" title="b5">w</font> implies <font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">v</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b5">w</font>,<font color="Olive" title="b4">v1</font> ) &amp; ( <font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">v</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b2">u1</font>,<font color="Olive" title="b4">v1</font> implies <font color="Olive" title="b3">v</font>,<font color="Olive" title="b1">u</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b4">v1</font>,<font color="Olive" title="b2">u1</font> ) &amp; ( <font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">v</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b2">u1</font>,<font color="Olive" title="b4">v1</font> &amp; <font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">v</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b4">v1</font>,<font color="Olive" title="b5">w</font> implies <font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">v</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b2">u1</font>,<font color="Olive" title="b5">w</font> ) &amp; (  not <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">v1</font> or <font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">v1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">u1</font> or <font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">v1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b2">u1</font>,<font color="Olive" title="b1">u</font> ) ) ) &amp; ( for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">C</font>  ex <font color="Olive" title="b4">u1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">C</font> st <br/>( <font color="Olive" title="b3">w</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">u1</font> &amp; <font color="Olive" title="b3">w</font>,<font color="Olive" title="b4">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font> ) ) &amp; ( for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">C</font>  ex <font color="Olive" title="b4">u1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">C</font> st <br/>( <font color="Olive" title="b3">w</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">u1</font> &amp; <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b3">w</font>,<font color="Olive" title="b4">u1</font> ) ) )
 <b>by </b><i><a class="txt" href="#E2:5_1_1"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="dirort.html#T1" target="_self" title="DIRORT:th.1">Th1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">DIRORT:def 1</a> <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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