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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="pnproc_1.html#M3" target="_self">Petri_net</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="pnproc_1.html#NM6">process</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>













<b>assume </b><a NAME="E1:120"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="pnproc_1.html#K12" target="_self">before</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being   <a href="pnproc_1.html#NM5">firing-sequence</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E3:120"/><i><font color="Green">E82</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="lang1.html#K1">^</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/>
<b>consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="pnproc_1.html#NM5">firing-sequence</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E5:120"/><i><font color="Green">E83</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> &amp; ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="finseq_1.html#NM4">FinSubsequence</a> st <br/>( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">b<sub>2</sub></font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> ) )
 <b>by </b><i><a class="txt" href="pnproc_1.html#E3:120"><i><font color="Green">E82</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font> being   <a href="finseq_1.html#NM4">FinSubsequence</a><b> such that </b><br/><a NAME="E7:120"/><i><font color="Green">E84</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>12</sub></font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="pnproc_1.html#E5:120"><i><font color="Green">E83</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="pnproc_1.html#NM5">firing-sequence</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E9:120"/><i><font color="Green">E85</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp; ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="finseq_1.html#NM4">FinSubsequence</a> st <br/>( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">b<sub>2</sub></font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> ) )
 <b>by </b><i><a class="txt" href="pnproc_1.html#E3:120"><i><font color="Green">E82</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font> being   <a href="finseq_1.html#NM4">FinSubsequence</a><b> such that </b><br/><a NAME="E11:120"/><i><font color="Green">E86</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>15</sub></font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="pnproc_1.html#E9:120"><i><font color="Green">E85</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>8</sub></font> <a href="lang1.html#K1">^</a> <font color="Maroon">c<sub>9</sub></font> as   <a href="pnproc_1.html#NM5">firing-sequence</a> of <font color="Maroon">c<sub>2</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>17</sub></font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>18</sub></font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>15</sub></font> as   <a href="finseq_1.html#NM4">FinSubsequence</a> ;<br/>
<a NAME="E14:120"/><i><font color="Green">E87</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E5:120"><i><font color="Green">E83</font></i></a>, <a class="txt" href="pnproc_1.html#E7:120"><i><font color="Green">E84</font></i></a>, <a class="txt" href="pnproc_1.html#E9:120"><i><font color="Green">E85</font></i></a>, <a class="txt" href="pnproc_1.html#E11:120"><i><font color="Green">E86</font></i></a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E15:120"/><b>then </b><i><font color="Green">E88</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>18</sub></font> )
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E93"><i><font color="Green">Lemma66</font></i></a></i>;<br/>
<a NAME="E16:120"/>
<font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>8</sub></font> <a href="lang1.html#K1">^</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_6.html#T12">FINSEQ_6:12</a></i>;<br/>
<a NAME="E17:120"/><b>then </b><i><font color="Green">E89</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>8</sub></font> <a href="lang1.html#K1">^</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>8</sub></font> <a href="lang1.html#K1">^</a> <font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E14:120"><i><font color="Green">E87</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>9</sub></font> as   <a href="finseq_1.html#NM4">FinSubsequence</a> ;<br/>
<a NAME="E19:120"/><i><font color="Green">E90</font></i>: 
( <font color="Maroon">c<sub>17</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>19</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>19</sub></font> )
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E14:120"><i><font color="Green">E87</font></i></a>, <a class="ref" href="pnproc_1.html#T70" target="_self">Th70</a></i>;<br/>
<a NAME="E20:120"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>8</sub></font> <a href="lang1.html#K1">^</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T71" target="_self">Th71</a></i>;<br/>
<a NAME="E21:120"/><b>then </b>
( <font color="Maroon">c<sub>17</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>8</sub></font> <a href="lang1.html#K1">^</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>8</sub></font> <a href="lang1.html#K1">^</a> <font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E19:120"><i><font color="Green">E90</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E22:120"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>17</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>12</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>18</sub></font> )
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E15:120"><i><font color="Green">E88</font></i></a>, <a class="txt" href="pnproc_1.html#E17:120"><i><font color="Green">E89</font></i></a>, <a class="ref" href="pnproc_1.html#T10" target="_self">Th10</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>17</sub></font>, <font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>12</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>18</sub></font> as   <a href="funct_1.html#NM1">Function</a> <b>by </b><i><a class="ref" href="grfunc_1.html#T31">GRFUNC_1:31</a></i>;<br/>
<a NAME="E24:120"/><i><font color="Green">E91</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>16</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E25:120"/>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>20</sub></font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>16</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>21</sub></font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>16</sub></font> )
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E14:120"><i><font color="Green">E87</font></i></a>, <a class="txt" href="pnproc_1.html#E92"><i><font color="Green">Lemma65</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>20</sub></font>, <font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>21</sub></font> as   <a href="finseq_1.html#NM4">FinSubsequence</a> <b>by </b><i><a class="txt" href="pnproc_1.html#E24:120"><i><font color="Green">E91</font></i></a>, <a class="ref" href="finseq_1.html#D12">FINSEQ_1:def 12</a></i>;<br/>
<i><font color="Green">E92</font></i>: <font color="Maroon">c<sub>22</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>23</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="pnproc_1.html#E5:120"><i><font color="Green">E83</font></i></a>, <a class="txt" href="pnproc_1.html#E7:120"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="pnproc_1.html#E9:120"><i><font color="Green">E85</font></i></a>, <a class="txt" href="pnproc_1.html#E11:120"><i><font color="Green">E86</font></i></a>, <a class="ref" href="pnproc_1.html#T73" target="_self">Th73</a></i>
<br/>.= 
<font color="Maroon">c<sub>16</sub></font>
<b>by </b><i><a class="ref" href="pnproc_1.html#T64" target="_self">Th64</a></i>
;<br/>
<a NAME="E28:120"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>23</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="120_2"><b>proof </b></a><div class="add">

<a NAME="E1:120_2"/>
( <font color="Maroon">c<sub>22</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>22</sub></font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E2:120_2"/><b>then </b><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E3:120_2"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E7:120"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E4:120_2"/>
( <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>14</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#R1">misses</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>15</sub></font> )
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E14:120"><i><font color="Green">E87</font></i></a>, <a class="txt" href="pnproc_1.html#E93"><i><font color="Green">Lemma66</font></i></a></i>;<br/>
<a NAME="E5:120_2"/><b>then </b><i><font color="Green">E96</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E6:120_2"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>14</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E11:120"><i><font color="Green">E86</font></i></a>, <a class="txt" href="pnproc_1.html#E14:120"><i><font color="Green">E87</font></i></a>, <a class="ref" href="pnproc_1.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E7:120_2"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T72" target="_self">Th72</a></i>;<br/>
<a NAME="E8:120_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>14</sub></font> <a href="xboole_0.html#R1">misses</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T8" target="_self">Th8</a></i>;<br/>
<b>hence </b><a NAME="E9:120_2"/>
<font color="Maroon">c<sub>22</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="txt" href="pnproc_1.html#E2:120_2"><i><font color="Green">E94</font></i></a>, <a class="txt" href="pnproc_1.html#E3:120_2"><i><font color="Green">E95</font></i></a>, <a class="txt" href="pnproc_1.html#E5:120_2"><i><font color="Green">E96</font></i></a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a><br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon">c<sub>24</sub></font> being   <a href="finseq_1.html#NM4">FinSubsequence</a><b> such that </b><br/><a NAME="E30:120"/><i><font color="Green">E94</font></i>: 
( <font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>22</sub></font> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>24</sub></font> )
 <b>by </b><i><a class="txt" href="pnproc_1.html#E14:120"><i><font color="Green">E87</font></i></a>, <a class="ref" href="pnproc_1.html#T82" target="_self">Th82</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>25</sub></font> being   <a href="finseq_1.html#NM4">FinSubsequence</a><b> such that </b><br/><a NAME="E32:120"/><i><font color="Green">E95</font></i>: 
( <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>23</sub></font> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>25</sub></font> )
 <b>by </b><i><a class="txt" href="pnproc_1.html#E14:120"><i><font color="Green">E87</font></i></a>, <a class="ref" href="pnproc_1.html#T82" target="_self">Th82</a></i>;<br/>
<a NAME="E33:120"/><i><font color="Green">E96</font></i>: 
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="pnproc_1.html#K12" target="_self">before</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E7:120"><i><font color="Green">E84</font></i></a>, <a class="txt" href="pnproc_1.html#E11:120"><i><font color="Green">E86</font></i></a>, <a class="txt" href="pnproc_1.html#E30:120"><i><font color="Green">E94</font></i></a></i>;<br/>
<a NAME="E34:120"/>
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="pnproc_1.html#K12" target="_self">before</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E7:120"><i><font color="Green">E84</font></i></a>, <a class="txt" href="pnproc_1.html#E11:120"><i><font color="Green">E86</font></i></a>, <a class="txt" href="pnproc_1.html#E32:120"><i><font color="Green">E95</font></i></a></i>;<br/>
<b>hence </b><a NAME="E35:120"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pnproc_1.html#K12" target="_self">before</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="pnproc_1.html#K13" target="_self">concur</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="pnproc_1.html#K12" target="_self">before</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E3:120"><i><font color="Green">E82</font></i></a>, <a class="txt" href="pnproc_1.html#E27:120"><i><font color="Green">E92</font></i></a>, <a class="txt" href="pnproc_1.html#E28:120"><i><font color="Green">E93</font></i></a>, <a class="txt" href="pnproc_1.html#E33:120"><i><font color="Green">E96</font></i></a></i>;<br/>


</div>
