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<b>consider </b><font color="Maroon">V</font> being   <a href="rlvect_1.html#NM2">RealLinearSpace</a>, <font color="Maroon">x</font> being   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">y</font> being   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E2:5_1_1"/><i><font color="Green">E20</font></i>: 
 <a href="analmetr.html#R1">Gen</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T7">ANALMETR:7</a></i>;<br/>
<b>take </b><font color="Maroon">C</font> =  <a href="analort.html#K6">CESpace</a> <font color="Maroon">V</font>,<font color="Maroon">x</font>,<font color="Maroon">y</font>;<br/>

<b>thus </b><a NAME="E3:5_1_1"/>
( ( for <font color="Olive">u</font>, <font color="Olive">u1</font>, <font color="Olive">v</font>, <font color="Olive">v1</font>, <font color="Olive">w</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">C</font> holds <br/> ( <font color="Olive">u</font>,<font color="Olive">u</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">v</font>,<font color="Olive">w</font> &amp; <font color="Olive">u</font>,<font color="Olive">v</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">w</font>,<font color="Olive">w</font> &amp; ( <font color="Olive">u</font>,<font color="Olive">v</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">u1</font>,<font color="Olive">v1</font> &amp; <font color="Olive">u</font>,<font color="Olive">v</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">v1</font>,<font color="Olive">u1</font> &amp; not <font color="Olive">u</font> <a href="hidden.html#R1">=</a> <font color="Olive">v</font> implies <font color="Olive">u1</font> <a href="hidden.html#R1">=</a> <font color="Olive">v1</font> ) &amp; ( <font color="Olive">u</font>,<font color="Olive">v</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">u1</font>,<font color="Olive">v1</font> &amp; <font color="Olive">u</font>,<font color="Olive">v</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">u1</font>,<font color="Olive">w</font> &amp; not <font color="Olive">u</font>,<font color="Olive">v</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">v1</font>,<font color="Olive">w</font> implies <font color="Olive">u</font>,<font color="Olive">v</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">w</font>,<font color="Olive">v1</font> ) &amp; ( <font color="Olive">u</font>,<font color="Olive">v</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">u1</font>,<font color="Olive">v1</font> implies <font color="Olive">v</font>,<font color="Olive">u</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">v1</font>,<font color="Olive">u1</font> ) &amp; ( <font color="Olive">u</font>,<font color="Olive">v</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">u1</font>,<font color="Olive">v1</font> &amp; <font color="Olive">u</font>,<font color="Olive">v</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">v1</font>,<font color="Olive">w</font> implies <font color="Olive">u</font>,<font color="Olive">v</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">u1</font>,<font color="Olive">w</font> ) &amp; (  not <font color="Olive">u</font>,<font color="Olive">u1</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">v</font>,<font color="Olive">v1</font> or <font color="Olive">v</font>,<font color="Olive">v1</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">u</font>,<font color="Olive">u1</font> or <font color="Olive">v</font>,<font color="Olive">v1</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">u1</font>,<font color="Olive">u</font> ) ) ) &amp; ( for <font color="Olive">u</font>, <font color="Olive">v</font>, <font color="Olive">w</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">C</font>  ex <font color="Olive">u1</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">C</font> st <br/>( <font color="Olive">w</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">u1</font> &amp; <font color="Olive">w</font>,<font color="Olive">u1</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">u</font>,<font color="Olive">v</font> ) ) &amp; ( for <font color="Olive">u</font>, <font color="Olive">v</font>, <font color="Olive">w</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">C</font>  ex <font color="Olive">u1</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">C</font> st <br/>( <font color="Olive">w</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">u1</font> &amp; <font color="Olive">u</font>,<font color="Olive">v</font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">w</font>,<font color="Olive">u1</font> ) ) )
 <b>by </b><i>, </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="dirort.html#D1" target="_self">DIRORT:def 1</a><br/>


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