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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">p</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</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">q</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</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">p1</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</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">q1</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">V</font>,<font color="Maroon">w</font>,<font color="Maroon">y</font></span>)</span>;<br/>













<b>assume </b><a NAME="E1:39"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">p1</font>,<font color="Maroon">q1</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">u</font> = <font color="Maroon">p</font>, <font color="Maroon">v</font> = <font color="Maroon">q</font>, <font color="Maroon">u1</font> = <font color="Maroon">p1</font>, <font color="Maroon">v1</font> = <font color="Maroon">q1</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font> ;<br/>
<a NAME="E3:39"/>
<font color="Maroon">u</font>,<font color="Maroon">v</font>,<font color="Maroon">u1</font>,<font color="Maroon">v1</font> <a href="analmetr.html#R3" target="_self">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:39"/><b>then </b>
<font color="Maroon">v</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font>,<font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u1</font> <a href="analmetr.html#R2" target="_self">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:39"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">v</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font>,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u1</font></span>)</span> <a href="analmetr.html#R2" target="_self">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 
<b>by </b><i/>;<br/>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u1</font></span>)</span> = 
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u1</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T29">RLVECT_1:29</a></i>
<br/>.= 
<font color="Maroon">u1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">v1</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T47">RLVECT_1:47</a></i>
;<br/>
<a NAME="E7:39"/><b>then </b>
<font color="Maroon">u</font>,<font color="Maroon">v</font>,<font color="Maroon">v1</font>,<font color="Maroon">u1</font> <a href="analmetr.html#R3" target="_self">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E8:39"/>
<font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">q1</font>,<font color="Maroon">p1</font>
 <b>by </b><i/>;<br/>


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