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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">x</font>, <font color="Olive" title="b2">y</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">x</font>,<font color="Olive" title="b2">y</font> holds <br/> <a href="analort.html#K6" title="ANALORT:func.6">CESpace</a> <font color="Maroon" title="c1">V</font>,<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> is   <a href="dirort.html#NM1" title="DIRORT:NM.1">Oriented_Orthogonality_Space</a></span><br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</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">x</font>,<font color="Maroon" title="c3">y</font> implies  <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> is   <a href="dirort.html#NM1" title="DIRORT:NM.1">Oriented_Orthogonality_Space</a> )</span><br/>





<b>assume </b><a NAME="E1:8"/>
 <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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <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> is   <a href="dirort.html#NM1" title="DIRORT:NM.1">Oriented_Orthogonality_Space</a></span><br/>

<a NAME="E2:8"/><b>then </b>
( ( 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>, <font color="Olive" title="b6">w1</font>, <font color="Olive" title="b7">w2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><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></span>)</span> 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 <span class="p1">(<span class="default"><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></span>)</span>  ex <font color="Olive" title="b4">u1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><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></span>)</span> 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 <span class="p1">(<span class="default"><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></span>)</span>  ex <font color="Olive" title="b4">u1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><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></span>)</span> 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="ref" href="dirort.html#T1" target="_self" title="DIRORT:th.1">Th1</a></i>;<br/>
<b>hence </b><a NAME="E3:8"/>
 <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> is   <a href="dirort.html#NM1" title="DIRORT:NM.1">Oriented_Orthogonality_Space</a>
 <b>by </b><i><a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</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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