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<b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">w</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u1</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v1</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u2</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v2</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/>

















<b>assume </b><b>that </b><br/><a NAME="E1:25"/><i><font color="Green">E45</font></i>: 
 <a href="analmetr.html#R1">Gen</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 <b>and </b><br/><a NAME="E2:25"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">u1</font>,<font color="Maroon">v1</font> <a href="geomtrap.html#R1" target="_self">'||'</a> <font color="Maroon">u</font>,<font color="Maroon">v</font> or <font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="geomtrap.html#R1" target="_self">'||'</a> <font color="Maroon">u1</font>,<font color="Maroon">v1</font> )
 <b>and </b><br/><a NAME="E3:25"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">u2</font>,<font color="Maroon">v2</font>,<font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> or <font color="Maroon">u</font>,<font color="Maroon">v</font>,<font color="Maroon">u2</font>,<font color="Maroon">v2</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 <b>and </b><br/><a NAME="E4:25"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">v</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">S</font> =  <a href="analmetr.html#K2">AMSpace</a> <font color="Maroon">V</font>,<font color="Maroon">w</font>,<font color="Maroon">y</font> as   <a href="analmetr.html#NM1">OrtAfSp</a> <b>by </b><i>, <a class="ref" href="analmetr.html#T44">ANALMETR:44</a></i>;<br/>
<b>reconsider </b><font color="Maroon">p'</font> = <font color="Maroon">u</font>, <font color="Maroon">q'</font> = <font color="Maroon">v</font>, <font color="Maroon">p1'</font> = <font color="Maroon">u1</font>, <font color="Maroon">q1'</font> = <font color="Maroon">v1</font>, <font color="Maroon">p2'</font> = <font color="Maroon">u2</font>, <font color="Maroon">q2'</font> = <font color="Maroon">v2</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2">AMSpace</a> <font color="Maroon">V</font>,<font color="Maroon">w</font>,<font color="Maroon">y</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T28">ANALMETR:28</a></i>;<br/>
<b>reconsider </b><font color="Maroon">p</font> = <font color="Maroon">p'</font>, <font color="Maroon">q</font> = <font color="Maroon">q'</font>, <font color="Maroon">p1</font> = <font color="Maroon">p1'</font>, <font color="Maroon">q1</font> = <font color="Maroon">q1'</font>, <font color="Maroon">p2</font> = <font color="Maroon">p2'</font>, <font color="Maroon">q2</font> = <font color="Maroon">q2'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> ;<br/>
<a NAME="E8:25"/><i><font color="Green">E72</font></i>: 
( <font color="Maroon">p2</font>,<font color="Maroon">q2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> or <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">p2</font>,<font color="Maroon">q2</font> )
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T31">ANALMETR:31</a></i>;<br/>
<a NAME="E9:25"/>
( <font color="Maroon">p1</font>,<font color="Maroon">q1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> or <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p1</font>,<font color="Maroon">q1</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E10:25"/><b>then </b>
( <font color="Maroon">p1</font>,<font color="Maroon">q1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">p2</font>,<font color="Maroon">q2</font> &amp; <font color="Maroon">p2</font>,<font color="Maroon">q2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">p1</font>,<font color="Maroon">q1</font> )
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E11:25"/>
( <font color="Maroon">u1</font>,<font color="Maroon">v1</font>,<font color="Maroon">u2</font>,<font color="Maroon">v2</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">u2</font>,<font color="Maroon">v2</font>,<font color="Maroon">u1</font>,<font color="Maroon">v1</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T31">ANALMETR:31</a></i>;<br/>


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