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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">x</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">u</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">v</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">w</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">w1</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><a NAME="E1:56"/><i><font color="Green">E39</font></i>: 
 <a href="analmetr.html#R1">Gen</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 ;<br/>

<b>assume </b><a NAME="E2:56"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">u</font>,<font color="Maroon">u1</font>,<font color="Maroon">v</font>,<font color="Maroon">v1</font> <a href="analort.html#R2" target="_self">are_COrtm_wrt</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">v</font>,<font color="Maroon">v1</font>,<font color="Maroon">w</font>,<font color="Maroon">w1</font> <a href="analort.html#R2" target="_self">are_COrtm_wrt</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">u2</font>,<font color="Maroon">v2</font>,<font color="Maroon">w</font>,<font color="Maroon">w1</font> <a href="analort.html#R2" target="_self">are_COrtm_wrt</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> )
 ;<br/>

<a NAME="E3:56"/><b>then </b>
 <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font>, <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u1</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">v</font>,<font color="Maroon">v1</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:56"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">v</font>,<font color="Maroon">v1</font> <a href="analoaf.html#R1">//</a>  <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font>, <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u1</font>
 
<b>by </b><i><a class="ref" href="analoaf.html#T21">ANALOAF:21</a></i>;<br/>
<a NAME="E5:56"/>
<font color="Maroon">w</font>,<font color="Maroon">w1</font>,<font color="Maroon">v</font>,<font color="Maroon">v1</font> <a href="analort.html#R2" target="_self">are_COrtm_wrt</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E6:56"/><b>then </b>
 <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">w</font>, <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">w1</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">v</font>,<font color="Maroon">v1</font>
 
<b>by </b><i/>;<br/>
<a NAME="E7:56"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">v</font>,<font color="Maroon">v1</font> <a href="analoaf.html#R1">//</a>  <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">w</font>, <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">w1</font>
 
<b>by </b><i><a class="ref" href="analoaf.html#T21">ANALOAF:21</a></i>;<br/>
<a NAME="E8:56"/>
<font color="Maroon">w</font>,<font color="Maroon">w1</font>,<font color="Maroon">u2</font>,<font color="Maroon">v2</font> <a href="analort.html#R2" target="_self">are_COrtm_wrt</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E9:56"/><b>then </b><i><font color="Green">E46</font></i>: 
 <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">w</font>, <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">w1</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">u2</font>,<font color="Maroon">v2</font>
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:56_1"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">w</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">w1</font> &amp; <font color="Maroon">v</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">v1</font> )
 ;<br/><a NAME="E2:56_1"/><b>then </b><i><font color="Green">E48</font></i>: 
 <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">w</font>, <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">w1</font> <a href="analoaf.html#R1">//</a>  <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font>, <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u1</font>
 <b>by </b><i>, , <a class="ref" href="analoaf.html#T20">ANALOAF:20</a></i>;<br/><a NAME="E3:56_1"/>
 <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">w</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">w1</font>
 <b>by </b><i>, , </i>;<br/><a NAME="E4:56_1"/><b>then </b>
 <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font>, <a href="analort.html#K2" target="_self">Ortm</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u1</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">u2</font>,<font color="Maroon">v2</font>
 <b>by </b><i>, <a class="txt" href="analort.html#E1"><i><font color="Green">Lemma38</font></i></a>, <a class="ref" href="analoaf.html#T20">ANALOAF:20</a></i>;<br/><b>hence </b><a NAME="E5:56_1"/>
( <font color="Maroon">u</font>,<font color="Maroon">u1</font>,<font color="Maroon">u2</font>,<font color="Maroon">v2</font> <a href="analort.html#R2" target="_self">are_COrtm_wrt</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> or <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v1</font> or <font color="Maroon">w</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w1</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:56"/>
( <font color="Maroon">u</font>,<font color="Maroon">u1</font>,<font color="Maroon">u2</font>,<font color="Maroon">v2</font> <a href="analort.html#R2" target="_self">are_COrtm_wrt</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> or <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v1</font> or <font color="Maroon">w</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w1</font> )
 ;<br/>


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