<?xml version="1.0"?>
<div class="add">

<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> be    <a href="pnproc_1.html#M4" target="_self">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>set </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K3">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> = <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pnproc_1.html#NM5">firing-sequence</a> of <font color="Maroon">c<sub>2</sub></font> : 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="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">b<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> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span> ) </span>}</span> ;<br/>
<b>thus </b><a NAME="E1:80"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span> <a href="pnproc_1.html#K13" target="_self">concur</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K4">*&gt;</a></span></span><a href="domain_1.html#K7">}</a></span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="80_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>10</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="E1:80_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span> <a href="pnproc_1.html#K13" target="_self">concur</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>11</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="E3:80_1"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</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>11</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> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span> ) )
 ;<br/>
<b>consider </b><font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> being   <a href="finseq_1.html#NM4">FinSubsequence</a><b> such that </b><br/><a NAME="E5:80_1"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>13</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> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span> )
 <b>by </b><i><a class="txt" href="pnproc_1.html#E3:80_1"><i><font color="Green">E50</font></i></a></i>;<br/>
<a NAME="E6:80_1"/><i><font color="Green">E52</font></i>: 
(  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> )
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E5:80_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>14</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E8:80_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K8">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K8">}</a></span>
 <b>by </b><i><a class="ref" href="pnproc_1.html#T4" target="_self">Th4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>15</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E10:80_1"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K8">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K8">}</a></span>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E6:80_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="pnproc_1.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E11:80_1"/><i><font color="Green">E55</font></i>: 
( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font> &amp; <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font> )
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E8:80_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="pnproc_1.html#E10:80_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E12:80_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K9">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span>,<span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K9">}</a></span>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E5:80_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="pnproc_1.html#E8:80_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="pnproc_1.html#E10:80_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>;<br/>
<a NAME="E13:80_1"/><b>then </b>
( ( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> ) or ( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> 2 ) or ( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> 1 ) )
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E14:80_1"/><b>then </b>
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> or <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> )
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E5:80_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="pnproc_1.html#E11:80_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="pnproc_1.html#E12:80_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="pnproc_1.html#T6" target="_self">Th6</a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<b>hence </b><a NAME="E15:80_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K4">*&gt;</a></span></span><a href="domain_1.html#K7">}</a></span>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E3:80_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>


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

<b>let </b><font color="Maroon">c<sub>10</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="E2:80"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K4">*&gt;</a></span></span><a href="domain_1.html#K7">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="80_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:80_2"/>
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> or <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> )
 </span><b>by </b><i><a class="txt" href="pnproc_1.html#E2:80"><i><font color="Green">E50</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="80_2_1"><b>suppose </b></a><a NAME="E1:80_2_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span>
 ;<br/><div class="add"><b>then </b><i><font color="Green">E52</font></i>: <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1"><a href="lang1.html#K9">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span>,<span class="p2"><a href="domain_1.html#K1">[</a><span class="default">2,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K9">}</a></span>
<b>by </b><i><a class="ref" href="pnproc_1.html#T6" target="_self">Th6</a></i>
<br/>.= 
<span class="p1"><a href="lang1.html#K8">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K8">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="lang1.html#K8">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">2,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K8">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>
;<br/><b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1"><a href="lang1.html#K8">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K8">}</a></span>, <font color="Maroon">c<sub>12</sub></font> = <span class="p1"><a href="lang1.html#K8">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">2,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K8">}</a></span> as   <a href="finseq_1.html#NM4">FinSubsequence</a> <b>by </b><i><a class="ref" href="pnproc_1.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E4:80_2_1"/>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default">1,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default">2,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K1">]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><a NAME="E5:80_2_1"/><b>then </b>
not <span class="p1"><a href="domain_1.html#K1">[</a><span class="default">1,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E6:80_2_1"/><b>then </b><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T56">ZFMISC_1:56</a></i>;<br/><a NAME="E7:80_2_1"/><i><font color="Green">E54</font></i>: 
(  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="pnproc_1.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E8:80_2_1"/>
( <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span> &amp; <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E9:80_2_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span> <a href="pnproc_1.html#K13" target="_self">concur</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E1:80_2_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="pnproc_1.html#E2:80_2_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="pnproc_1.html#E6:80_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="pnproc_1.html#E7:80_2_1"><i><font color="Green">E54</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="80_2_2"><b>suppose </b></a><a NAME="E1:80_2_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K4">*&gt;</a></span>
 ;<br/><div class="add"><b>then </b><i><font color="Green">E52</font></i>: <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1"><a href="lang1.html#K9">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K1">]</a></span>,<span class="p2"><a href="domain_1.html#K1">[</a><span class="default">2,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K9">}</a></span>
<b>by </b><i><a class="ref" href="pnproc_1.html#T6" target="_self">Th6</a></i>
<br/>.= 
<span class="p1"><a href="lang1.html#K8">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K8">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="lang1.html#K8">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">2,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K8">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>
;<br/><b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1"><a href="lang1.html#K8">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">2,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K8">}</a></span>, <font color="Maroon">c<sub>12</sub></font> = <span class="p1"><a href="lang1.html#K8">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K1">]</a></span></span><a href="lang1.html#K8">}</a></span> as   <a href="finseq_1.html#NM4">FinSubsequence</a> <b>by </b><i><a class="ref" href="pnproc_1.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E4:80_2_2"/>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default">1,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default">2,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><a NAME="E5:80_2_2"/><b>then </b>
not <span class="p1"><a href="domain_1.html#K1">[</a><span class="default">2,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E6:80_2_2"/><b>then </b><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T56">ZFMISC_1:56</a></i>;<br/><a NAME="E7:80_2_2"/><i><font color="Green">E54</font></i>: 
(  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="pnproc_1.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E8:80_2_2"/>
( <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span> &amp; <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E9:80_2_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span> <a href="pnproc_1.html#K13" target="_self">concur</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3">*&gt;</a></span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E1:80_2_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="pnproc_1.html#E2:80_2_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="pnproc_1.html#E6:80_2_2"><i><font color="Green">E53</font></i></a>, <a class="txt" href="pnproc_1.html#E7:80_2_2"><i><font color="Green">E54</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
