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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">OAS</font> be   <a href="analoaf.html#NM1">OAffinSpace</a>;<br/>



<b>assume </b><a NAME="E1:6"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">OAS</font> <a href="hidden.html#R1">=</a>  <a href="analoaf.html#K2">OASpace</a> <font color="Maroon">V</font>
 ;<br/>

<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font>, <font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font>, <font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</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>, <font color="Maroon">v</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">w</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">y</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/>



<b>assume </b><a NAME="E2:6"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 ;<br/>

<div><i><font color="Green">E38</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:6_1"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 ;<br/><a NAME="E2:6_1"/><b>then </b>
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> or <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">c</font> )
 <b>by </b><i><a class="ref" href="diraf.html#D4">DIRAF:def 4</a></i>;<br/><a NAME="E3:6_1"/><b>then </b>
( <font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> or <font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">y</font>,<font color="Maroon">w</font> )
 <b>by </b><i>, , <a class="ref" href="geomtrap.html#T2">GEOMTRAP:2</a></i>;<br/><b>hence </b><a NAME="E4:6_1"/>
<font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="geomtrap.html#R1">'||'</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="geomtrap.html#D1">GEOMTRAP:def 1</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:6_2"/>
<font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="geomtrap.html#R1">'||'</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 ;<br/><a NAME="E2:6_2"/><b>then </b>
( <font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> or <font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">y</font>,<font color="Maroon">w</font> )
 <b>by </b><i><a class="ref" href="geomtrap.html#D1">GEOMTRAP:def 1</a></i>;<br/><a NAME="E3:6_2"/><b>then </b>
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> or <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">c</font> )
 <b>by </b><i>, , <a class="ref" href="geomtrap.html#T2">GEOMTRAP:2</a></i>;<br/><b>hence </b><a NAME="E4:6_2"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="diraf.html#D4">DIRAF:def 4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:6"/>
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> iff <font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="geomtrap.html#R1">'||'</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 <b>by </b><i/>;<br/>


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