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<b>consider </b><font color="Maroon">c<sub>1</sub></font> being   <a href="rlvect_1.html#NM2">RealLinearSpace</a><b> such that </b><br/><a NAME="E2:93_1_1"/><i><font color="Green">E82</font></i>: 
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>1</sub></font> st  <a href="analmetr.html#R1">Gen</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T7">ANALMETR:7</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> being   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:93_1_1"/><i><font color="Green">E83</font></i>: 
 <a href="analmetr.html#R1">Gen</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="geomtrap.html#E2:93_1_1"><i><font color="Green">E82</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="geomtrap.html#K7" target="_self">DTrSpace</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>;<br/>
<a NAME="E5:93_1_1"/>
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>, <font color="Olive">b<sub>9</sub></font>, <font color="Olive">b<sub>10</sub></font> being  <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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="geomtrap.html#K9" target="_self">#</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="geomtrap.html#K9" target="_self">#</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>4</sub></font></span>)</span> &amp; ex <font color="Olive">b<sub>11</sub></font> being  <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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> st <font color="Olive">b<sub>11</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <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> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>3</sub></font> implies <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <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="analoaf.html#R2">//</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="analoaf.html#R2">//</a> <font color="Olive">b<sub>1</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>4</sub></font> ) &amp; (  not <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>3</sub></font>,<font color="Olive">b<sub>4</sub></font> or <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>1</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>3</sub></font> or <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>2</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>4</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>3</sub></font>,<font color="Olive">b<sub>4</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="geomtrap.html#K9" target="_self">#</a> <font color="Olive">b<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>9</sub></font> implies <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> ) &amp; ( <font color="Olive">b<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>10</sub></font> &amp; <font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>5</sub></font> &amp; <font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>7</sub></font> &amp; <font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>8</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>3</sub></font>,<font color="Olive">b<sub>4</sub></font> implies <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> ) &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>2</sub></font>,<font color="Olive">b<sub>3</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>2</sub></font> <a href="hidden.html#R1">=</a> <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="analoaf.html#R2">//</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; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>2</sub></font> implies <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> ) &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>3</sub></font>,<font color="Olive">b<sub>4</sub></font> implies ( <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>3</sub></font> ) ) &amp; ex <font color="Olive">b<sub>11</sub></font> being  <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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> st <br/>( <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>3</sub></font>,<font color="Olive">b<sub>11</sub></font> or <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>11</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="analoaf.html#R2">//</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>9</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>3</sub></font>,<font color="Olive">b<sub>10</sub></font> &amp; not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> implies <font color="Olive">b<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>10</sub></font> ) )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E4:93_1_1"><i><font color="Green">E83</font></i></a>, <a class="txt" href="geomtrap.html#E81"><i><font color="Green">Lemma67</font></i></a>, <a class="txt" href="geomtrap.html#E82"><i><font color="Green">Lemma68</font></i></a>, <a class="txt" href="geomtrap.html#E83"><i><font color="Green">Lemma69</font></i></a>, <a class="txt" href="geomtrap.html#E84"><i><font color="Green">Lemma70</font></i></a>, <a class="txt" href="geomtrap.html#E85"><i><font color="Green">Lemma71</font></i></a>, <a class="txt" href="geomtrap.html#E86"><i><font color="Green">Lemma72</font></i></a>, <a class="txt" href="geomtrap.html#E87"><i><font color="Green">Lemma73</font></i></a>, <a class="txt" href="geomtrap.html#E88"><i><font color="Green">Lemma74</font></i></a>, <a class="txt" href="geomtrap.html#E89"><i><font color="Green">Lemma75</font></i></a>, <a class="txt" href="geomtrap.html#E90"><i><font color="Green">Lemma76</font></i></a>, <a class="txt" href="geomtrap.html#E91"><i><font color="Green">Lemma77</font></i></a>, <a class="txt" href="geomtrap.html#E92"><i><font color="Green">Lemma78</font></i></a>, <a class="txt" href="geomtrap.html#E93"><i><font color="Green">Lemma79</font></i></a>, <a class="txt" href="geomtrap.html#E94"><i><font color="Green">Lemma80</font></i></a></i>;<br/>
<a NAME="E6:93_1_1"/><b>then </b>
 <a href="geomtrap.html#K7" target="_self">DTrSpace</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> is <a href="geomtrap.html#V2" target="_self">MidOrdTrapSpace-like</a>
 
<b>by </b><i><a class="ref" href="geomtrap.html#D13" target="_self">Def13</a></i>;<br/>
<b>hence </b><a NAME="E7:93_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being non <a href="struct_0.html#V3">empty</a>  <a href="geomtrap.html#L1" target="_self">AfMidStruct</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="geomtrap.html#V1" target="_self">strict</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="geomtrap.html#V2" target="_self">MidOrdTrapSpace-like</a> )
 ;<br/>


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