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<div class="add">

<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>assume </b><a NAME="E1:2"/><i><font color="Green">E2</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>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="analort.html#K6">CESpace</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="E2:2"/><i><font color="Green">E3</font></i>: 
 <a href="analort.html#K6">CESpace</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> <a href="hidden.html#R1">=</a>  <a href="analoaf.html#G1">AffinStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="analort.html#K4">CORTE</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> #)
 
<b>by </b><i><a class="ref" href="analort.html#D7">ANALORT:def 7</a></i>;<br/>
<b>thus </b><a NAME="E3:2"/>
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> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analort.html#K6">CESpace</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>,<font color="Olive">b<sub>1</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>5</sub></font> &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>5</sub></font> &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>4</sub></font> &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>2</sub></font> &amp; not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</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>4</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>4</sub></font> &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>5</sub></font> &amp; not <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font> implies <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>4</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>4</sub></font> implies <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>2</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>4</sub></font> &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font> implies <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>5</sub></font> ) &amp; (  not <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> or <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> or <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analort.html#K6">CESpace</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>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>8</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="dirort.html#E2:2"><i><font color="Green">E3</font></i></a></i>;<br/>
<b>thus </b><a NAME="E2:2_1"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:2_1_1"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analort.html#R1">are_COrte_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="analort.html#T20">ANALORT:20</a></i>;<br/>
<b>hence </b><a NAME="E2:2_1_1"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="analort.html#T56">ANALORT:56</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:2_1"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:2_1_2"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analort.html#R1">are_COrte_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="analort.html#T22">ANALORT:22</a></i>;<br/>
<b>hence </b><a NAME="E2:2_1_2"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="analort.html#T56">ANALORT:56</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E4:2_1"/>
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> implies <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:2_1_3"/>
( <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analort.html#R1">are_COrte_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>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analort.html#R1">are_COrte_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; not <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> implies <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> )
 
<b>by </b><i><a class="txt" href="dirort.html#E1:2"><i><font color="Green">E2</font></i></a>, <a class="ref" href="analort.html#T30">ANALORT:30</a></i>;<br/>
<b>hence </b><a NAME="E2:2_1_3"/>
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> implies <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="ref" href="analort.html#T56">ANALORT:56</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E5:2_1"/>
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> implies <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_4"><b>proof </b></a><div class="add">

<a NAME="E1:2_1_4"/>
( <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analort.html#R1">are_COrte_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>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analort.html#R1">are_COrte_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; not <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analort.html#R1">are_COrte_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analort.html#R1">are_COrte_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="dirort.html#E1:2"><i><font color="Green">E2</font></i></a>, <a class="ref" href="analort.html#T32">ANALORT:32</a></i>;<br/>
<b>hence </b><a NAME="E2:2_1_4"/>
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> implies <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="ref" href="analort.html#T56">ANALORT:56</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E6:2_1"/>
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> implies <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_5"><b>proof </b></a><div class="add">

<a NAME="E1:2_1_5"/>
( <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analort.html#R1">are_COrte_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analort.html#R1">are_COrte_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="analort.html#T34">ANALORT:34</a></i>;<br/>
<b>hence </b><a NAME="E2:2_1_5"/>
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> implies <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="ref" href="analort.html#T56">ANALORT:56</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E7:2_1"/>
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> implies <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_6"><b>proof </b></a><div class="add">

<a NAME="E1:2_1_6"/>
( <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analort.html#R1">are_COrte_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>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analort.html#R1">are_COrte_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analort.html#R1">are_COrte_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="dirort.html#E1:2"><i><font color="Green">E2</font></i></a>, <a class="ref" href="analort.html#T36">ANALORT:36</a></i>;<br/>
<b>hence </b><a NAME="E2:2_1_6"/>
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> implies <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="ref" href="analort.html#T56">ANALORT:56</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E8:2_1"/>
(  not <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> or <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_7"><b>proof </b></a><div class="add">

<a NAME="E1:2_1_7"/>
(  not <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analort.html#R1">are_COrte_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analort.html#R1">are_COrte_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analort.html#R1">are_COrte_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="dirort.html#E1:2"><i><font color="Green">E2</font></i></a>, <a class="ref" href="analort.html#T18">ANALORT:18</a></i>;<br/>
<b>hence </b><a NAME="E2:2_1_7"/>
(  not <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> or <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="ref" href="analort.html#T56">ANALORT:56</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E9:2_1"/>
verum
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E4:2"/>
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="analort.html#K6">CESpace</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>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="analort.html#K6">CESpace</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>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>4</sub></font> &amp; <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_2"><b>proof </b></a><div class="add">

<b>let </b><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="analort.html#K6">CESpace</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>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>10</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> <b>by </b><i><a class="txt" href="dirort.html#E2:2"><i><font color="Green">E3</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:2_2"/><i><font color="Green">E4</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analort.html#R1">are_COrte_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="dirort.html#E1:2"><i><font color="Green">E2</font></i></a>, <a class="ref" href="analort.html#T38">ANALORT:38</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>11</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analort.html#K6">CESpace</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> <b>by </b><i><a class="txt" href="dirort.html#E2:2"><i><font color="Green">E3</font></i></a></i>;<br/>
<a NAME="E5:2_2"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="dirort.html#E3:2_2"><i><font color="Green">E4</font></i></a>, <a class="ref" href="analort.html#T56">ANALORT:56</a></i>;<br/>
<b>hence </b><a NAME="E6:2_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analort.html#K6">CESpace</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="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 ;<br/>


</div><b>end;</b></div>

<b>let </b><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="analort.html#K6">CESpace</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>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>10</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> <b>by </b><i><a class="txt" href="dirort.html#E2:2"><i><font color="Green">E3</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E7:2"/><i><font color="Green">E4</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> &amp; <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="analort.html#R1">are_COrte_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="dirort.html#E1:2"><i><font color="Green">E2</font></i></a>, <a class="ref" href="analort.html#T40">ANALORT:40</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>11</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analort.html#K6">CESpace</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> <b>by </b><i><a class="txt" href="dirort.html#E2:2"><i><font color="Green">E3</font></i></a></i>;<br/>
<a NAME="E9:2"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>12</sub></font> )
 
<b>by </b><i><a class="txt" href="dirort.html#E7:2"><i><font color="Green">E4</font></i></a>, <a class="ref" href="analort.html#T56">ANALORT:56</a></i>;<br/>
<b>hence </b><a NAME="E10:2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analort.html#K6">CESpace</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="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="dirort.html#NR1" target="_self">'//'</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Olive">b<sub>1</sub></font> )
 ;<br/>


</div>
