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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/>













<b>assume </b><b>that </b><br/><a NAME="E1:46"/><i><font color="Green">E38</font></i>: 
 <a href="analmetr.html#R1" target="_self">Gen</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:46"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E3:46"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>7</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E5:46"/>
( <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analmetr.html#R3" target="_self">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analmetr.html#R3" target="_self">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E2:46"><i><font color="Green">E39</font></i></a>, <a class="txt" href="analmetr.html#E3:46"><i><font color="Green">E40</font></i></a>, <a class="ref" href="analmetr.html#T31" target="_self">Th31</a></i>;<br/>
<a NAME="E6:46"/><b>then </b><i><font color="Green">E41</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R2" target="_self">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>11</sub></font> <a href="analmetr.html#R2" target="_self">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#D3" target="_self">Def3</a></i>;<br/>
<div><i><font color="Green">E42</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>14</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>13</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T81">VECTSP_1:81</a></i>
<br/>.= 
<font color="Maroon">c<sub>14</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="ref" href="analoaf.html#T4">ANALOAF:4</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E8:46"/><b>then </b><i><font color="Green">E43</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>10</sub></font>
 
;<br/>
<a NAME="E9:46"/><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E7:46"><i><font color="Green">E42</font></i></a></i>;<br/>
<a NAME="E10:46"/><i><font color="Green">E45</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E7:46"><i><font color="Green">E42</font></i></a></i>;<br/>
<a NAME="E11:46"/>
<font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>11</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="analmetr.html#R2" target="_self">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E1:46"><i><font color="Green">E38</font></i></a>, <a class="txt" href="analmetr.html#E6:46"><i><font color="Green">E41</font></i></a>, <a class="txt" href="analmetr.html#E8:46"><i><font color="Green">E43</font></i></a>, <a class="txt" href="analmetr.html#E9:46"><i><font color="Green">E44</font></i></a>, <a class="ref" href="analmetr.html#T16" target="_self">Th16</a></i>;<br/>
<a NAME="E12:46"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R3" target="_self">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E10:46"><i><font color="Green">E45</font></i></a>, <a class="ref" href="analmetr.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E13:46"/>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T31" target="_self">Th31</a></i>;<br/>


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