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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">a</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K7" target="_self">DTrSpace</a> <font color="Maroon">V</font>,<font color="Maroon">w</font>,<font color="Maroon">y</font></span>)</span>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K7" target="_self">DTrSpace</a> <font color="Maroon">V</font>,<font color="Maroon">w</font>,<font color="Maroon">y</font></span>)</span>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K7" target="_self">DTrSpace</a> <font color="Maroon">V</font>,<font color="Maroon">w</font>,<font color="Maroon">y</font></span>)</span>;<br/><b>let </b><font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K7" target="_self">DTrSpace</a> <font color="Maroon">V</font>,<font color="Maroon">w</font>,<font color="Maroon">y</font></span>)</span>;<br/>













<b>assume </b><a NAME="E1:85"/><i><font color="Green">E45</font></i>: 
 <a href="analmetr.html#R1">Gen</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">u</font> = <font color="Maroon">a</font>, <font color="Maroon">u1</font> = <font color="Maroon">b</font>, <font color="Maroon">v</font> = <font color="Maroon">c</font>, <font color="Maroon">v1</font> = <font color="Maroon">d</font> as   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font> ;<br/>
<b>set </b><font color="Maroon">ab</font> = <font color="Maroon">a</font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Maroon">b</font>;<br/>
<b>set </b><font color="Maroon">cd</font> = <font color="Maroon">c</font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Maroon">d</font>;<br/>
<b>set </b><font color="Maroon">ac</font> = <font color="Maroon">a</font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Maroon">c</font>;<br/>
<b>set </b><font color="Maroon">bd</font> = <font color="Maroon">b</font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Maroon">d</font>;<br/>
<b>set </b><font color="Maroon">uu1</font> = <font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">u1</font>;<br/>
<b>set </b><font color="Maroon">vv1</font> = <font color="Maroon">v</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v1</font>;<br/>
<b>set </b><font color="Maroon">uv</font> = <font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font>;<br/>
<b>set </b><font color="Maroon">u1v1</font> = <font color="Maroon">u1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v1</font>;<br/>
<a NAME="E3:85"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">a</font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">u1</font> &amp; <font color="Maroon">c</font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v1</font> &amp; <font color="Maroon">a</font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font> &amp; <font color="Maroon">b</font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v1</font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E22"><i><font color="Green">Lemma75</font></i></a>, <a class="ref" href="geomtrap.html#T15" target="_self">Th15</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Maroon">b</font></span>)</span> <a href="geomtrap.html#K9" target="_self">#</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Maroon">d</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">u1</font></span>)</span> <a href="geomtrap.html#K1" target="_self">#</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v1</font></span>)</span>
<b>by </b><i><a class="txt" href="geomtrap.html#E22"><i><font color="Green">Lemma75</font></i></a>, <a class="ref" href="geomtrap.html#T15" target="_self">Th15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font></span>)</span> <a href="geomtrap.html#K1" target="_self">#</a> <span class="p1">(<span class="default"><font color="Maroon">u1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v1</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Maroon">c</font></span>)</span> <a href="geomtrap.html#K9" target="_self">#</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Maroon">d</font></span>)</span>
<b>by </b><i><a class="txt" href="geomtrap.html#E22"><i><font color="Green">Lemma75</font></i></a>, <a class="txt" href="geomtrap.html#E23"><i><font color="Green">Lemma76</font></i></a>, <a class="ref" href="geomtrap.html#T15" target="_self">Th15</a></i>
;<br/><br/>


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