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<b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>7</sub></font>;<br/>





<b>assume </b><a NAME="E1:57"/><i><font color="Green">E47</font></i>: 
 <a href="analmetr.html#R1" target="_self">Gen</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>;<br/>
<a NAME="E2:57"/><i><font color="Green">E48</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font>, <font color="Olive">b<sub>6</sub></font>, <font color="Olive">b<sub>7</sub></font>, <font color="Olive">b<sub>8</sub></font> being  <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>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> holds <br/>( ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> implies ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> ) ) &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font> &amp; not <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font> &amp; not <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) )
 
<b>by </b><i><a class="txt" href="analmetr.html#E1:57"><i><font color="Green">E47</font></i></a>, <a class="ref" href="analmetr.html#T33" target="_self">Th33</a>, <a class="ref" href="analmetr.html#T34" target="_self">Th34</a>, <a class="ref" href="analmetr.html#T35" target="_self">Th35</a>, <a class="ref" href="analmetr.html#T36" target="_self">Th36</a>, <a class="ref" href="analmetr.html#T38" target="_self">Th38</a>, <a class="ref" href="analmetr.html#T40" target="_self">Th40</a></i>;<br/>
<a NAME="E3:57"/><i><font color="Green">E49</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <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>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span>ex <font color="Olive">b<sub>4</sub></font> being  <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>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E1:57"><i><font color="Green">E47</font></i></a>, <a class="ref" href="analmetr.html#T37" target="_self">Th37</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> =  <a href="analoaf.html#G1">AffinStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span>,the <a href="analoaf.html#U1">CONGR</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> #);<br/>
<a NAME="E4:57"/>
 <a href="analoaf.html#G1">AffinStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span>,the <a href="analoaf.html#U1">CONGR</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> #) <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K3" target="_self">Af</a> <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span>
 
;<br/>
<a NAME="E5:57"/><b>then </b><i><font color="Green">E50</font></i>: 
 <a href="analoaf.html#G1">AffinStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span>,the <a href="analoaf.html#U1">CONGR</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> #) <a href="hidden.html#R1">=</a>  <a href="diraf.html#K2">Lambda</a> <span class="p1">(<span class="default"><a href="analoaf.html#K2">OASpace</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="analmetr.html#T30" target="_self">Th30</a></i>;<br/>
<a NAME="E6:57"/>
( ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> st <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>7</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 ) ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>7</sub></font>ex <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> ) )
 
<b>by </b><i><a class="txt" href="analmetr.html#E1:57"><i><font color="Green">E47</font></i></a>, <a class="ref" href="analmetr.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E7:57"/><b>then </b>
 <a href="analoaf.html#K2">OASpace</a> <font color="Maroon">c<sub>7</sub></font> is   <a href="analoaf.html#NM2">OAffinPlane</a>
 
<b>by </b><i><a class="ref" href="analoaf.html#T51">ANALOAF:51</a></i>;<br/>
<a NAME="E8:57"/><b>then </b>
 <a href="analoaf.html#G1">AffinStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span>,the <a href="analoaf.html#U1">CONGR</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> #) is   <a href="diraf.html#NM2">AffinPlane</a>
 
<b>by </b><i><a class="txt" href="analmetr.html#E5:57"><i><font color="Green">E50</font></i></a>, <a class="ref" href="diraf.html#T53">DIRAF:53</a></i>;<br/>
<b>hence </b><a NAME="E9:57"/>
 <a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> is   <a href="analmetr.html#NM2">OrtAfPl</a>
 <b>by </b><i><a class="txt" href="analmetr.html#E2:57"><i><font color="Green">E48</font></i></a>, <a class="txt" href="analmetr.html#E3:57"><i><font color="Green">E49</font></i></a>, <a class="ref" href="analmetr.html#D10" target="_self">Def10</a></i>;<br/>


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