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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V6">finite</a>  <a href="fsm_1.html#L2" target="_self">Mealy-FSM</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V6">finite</a> <a href="fsm_1.html#V5" target="_self">reduced</a> <a href="fsm_1.html#V7" target="_self">connected</a>  <a href="fsm_1.html#L2" target="_self">Mealy-FSM</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>









<b>set </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>5</sub></font>;<br/>
<b>assume </b><a NAME="E1:113"/><i><font color="Green">E83</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#R1">misses</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="fsm_1.html#R4" target="_self">-are_equivalent</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="fsm_1.html#K13" target="_self">-Mealy_union</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E2:113"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="fsm_1.html#NM1">State</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> st <br/>for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Olive">b<sub>1</sub></font> holds <br/>(  not <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> or  not <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> or ex <font color="Olive">b<sub>4</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Olive">b<sub>1</sub></font> st <br/>( not <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> &amp; not <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> ) )
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">c<sub>3</sub></font></span>)</span><b> such that </b><br/><a NAME="E4:113"/><i><font color="Green">E84</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>8</sub></font> holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> or  not <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> or ex <font color="Olive">b<sub>3</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>8</sub></font> st <br/>( not <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; not <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) )
 ;<br/>
<a NAME="E5:113"/><i><font color="Green">E85</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> = the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>13</sub></font> = the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>5</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>14</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>15</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/>
<a NAME="E6:113"/><i><font color="Green">E86</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="fsm_1.html#K8" target="_self">final_states_partition</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="fsm_1.html#D18" target="_self">Def18</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>8</sub></font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E8:113"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
;<br/>
<a NAME="E9:113"/><b>then </b><i><font color="Green">E87</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a>  <a href="fsm_1.html#K8" target="_self">final_states_partition</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="fsm_1.html#D18" target="_self">Def18</a></i>;<br/>
<a NAME="E10:113"/><b>then </b><i><font color="Green">E88</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>17</sub></font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E12:113"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/>
 <a href="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><a href="fsm_1.html#K8" target="_self">final_states_partition</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="ref" href="fsm_1.html#D24" target="_self">Def24</a></i>
;<br/>
<a NAME="E14:113"/><b>then </b><i><font color="Green">E90</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E6:113"><i><font color="Green">E86</font></i></a>, <a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:113_2"/>
( <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> )
 </span><b>by </b><i><a class="txt" href="fsm_1.html#E12:113"><i><font color="Green">E89</font></i></a>, <a class="txt" href="fsm_1.html#E14:113"><i><font color="Green">E90</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_1"><b>suppose </b></a><a NAME="E1:113_2_1"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>17</sub></font></span><a href="domain_1.html#K6">}</a></span>;<br/><div><i><font color="Green">E92</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_1_1"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>17</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>17</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_1"><i><font color="Green">E91</font></i></a></i>;<br/><a NAME="E3:113_2_1_1"/>
<font color="Maroon">c<sub>19</sub></font> is <a href="fsm_1.html#V6" target="_self">accessible</a>
 <b>by </b><i><a class="ref" href="fsm_1.html#D22" target="_self">Def22</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>20</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:113_2_1_1"/><i><font color="Green">E94</font></i>: 
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="fsm_1.html#R1" target="_self">-leads_to</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="ref" href="fsm_1.html#D21" target="_self">Def21</a></i>;<br/><b>set </b><font color="Maroon">c<sub>21</sub></font> = the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>5</sub></font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">c<sub>20</sub></font>;<br/><div><i><font color="Green">E95</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_1_1_1"/><i><font color="Green">E96</font></i>: 
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>5</sub></font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/><a NAME="E2:113_2_1_1_1"/>
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>5</sub></font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E5:113"><i><font color="Green">E85</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E3:113_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_1_1"><i><font color="Green">E93</font></i></a>, <a class="txt" href="fsm_1.html#E1:113_2_1_1_1"><i><font color="Green">E96</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_1_1_2"/><i><font color="Green">E96</font></i>: 
not the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>5</sub></font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/><a NAME="E2:113_2_1_1_2"/><i><font color="Green">E97</font></i>: 
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>5</sub></font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>19</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/><b>reconsider </b><font color="Maroon">c<sub>23</sub></font> = the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>5</sub></font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">c<sub>20</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="txt" href="fsm_1.html#E2:113_2_1_1_2"><i><font color="Green">E97</font></i></a>, <a class="ref" href="fsm_1.html#D24" target="_self">Def24</a></i>;<br/><a NAME="E5:113_2_1_1_2"/><i><font color="Green">E98</font></i>: 
 <a href="fsm_1.html#K8" target="_self">final_states_partition</a> <font color="Maroon">c<sub>3</sub></font> is <a href="fsm_1.html#V4" target="_self">final</a>
 <b>by </b><i><a class="ref" href="fsm_1.html#D15" target="_self">Def15</a></i>;<br/><a NAME="E6:113_2_1_1_2"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> holds <br/>(  not <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> or  not <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_1_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:113_2_1_1_2_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> )
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>24</sub></font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">c<sub>3</sub></font></span>)</span><b> such that </b><br/><a NAME="E3:113_2_1_1_2_1"/><i><font color="Green">E99</font></i>: 
( <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font> )
 ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>24</sub></font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E6:113"><i><font color="Green">E86</font></i></a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>16</sub></font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/>
<a NAME="E6:113_2_1_1_2_1"/>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
;<br/>
<a NAME="E7:113_2_1_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a>  <a href="fsm_1.html#K8" target="_self">final_states_partition</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="fsm_1.html#D18" target="_self">Def18</a></i>;<br/>
<a NAME="E8:113_2_1_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>25</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>26</sub></font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E9:113"><i><font color="Green">E87</font></i></a>, <a class="txt" href="fsm_1.html#E1:113_2_1_1_2"><i><font color="Green">E96</font></i></a>, <a class="txt" href="fsm_1.html#E3:113_2_1_1_2_1"><i><font color="Green">E99</font></i></a>, <a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E9:113_2_1_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E12:113"><i><font color="Green">E89</font></i></a>, <a class="txt" href="fsm_1.html#E3:113_2_1_1_2_1"><i><font color="Green">E99</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>


</div><b>end;</b></div><a NAME="E7:113_2_1_1_2"/><b>then </b>
not <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="fsm_1.html#R5" target="_self">-are_equivalent</a> 
 <b>by </b><i><a class="txt" href="fsm_1.html#E6:113"><i><font color="Green">E86</font></i></a>, <a class="txt" href="fsm_1.html#E5:113_2_1_1_2"><i><font color="Green">E98</font></i></a>, <a class="ref" href="fsm_1.html#D14" target="_self">Def14</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>24</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E9:113_2_1_1_2"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i><a class="ref" href="fsm_1.html#D10" target="_self">Def10</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>23</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> ;<br/><b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>22</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> ;<br/><a NAME="E12:113_2_1_1_2"/><i><font color="Green">E100</font></i>: 
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="fsm_1.html#R1" target="_self">-leads_to</a> <font color="Maroon">c<sub>25</sub></font>
 <b>by </b><i><a class="ref" href="fsm_1.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E13:113_2_1_1_2"/>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="ref" href="fsm_1.html#T72" target="_self">Th72</a></i>;<br/><a NAME="E14:113_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="txt" href="fsm_1.html#E9:113_2_1_1_2"><i><font color="Green">E99</font></i></a>, <a class="ref" href="fsm_1.html#T74" target="_self">Th74</a></i>;<br/><a NAME="E15:113_2_1_1_2"/><b>then </b>
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i><a class="txt" href="fsm_1.html#E5:113_2_1_1"><i><font color="Green">E94</font></i></a>, <a class="txt" href="fsm_1.html#E12:113_2_1_1_2"><i><font color="Green">E100</font></i></a>, <a class="ref" href="fsm_1.html#T27" target="_self">Th27</a></i>;<br/><b>hence </b><a NAME="E16:113_2_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="ref" href="fsm_1.html#D9" target="_self">Def9</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:113_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E6:113_2_1_1"><i><font color="Green">E95</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_1_2"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>17</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:113_2_1_2"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>17</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>16</sub></font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/><b>reconsider </b><font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>17</sub></font></span><a href="domain_1.html#K6">}</a></span> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/><b>consider </b><font color="Maroon">c<sub>21</sub></font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E6:113_2_1_2"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_1_2"><i><font color="Green">E93</font></i></a>, <a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/><a NAME="E7:113_2_1_2"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E14:113"><i><font color="Green">E90</font></i></a>, <a class="txt" href="fsm_1.html#E2:113_2_1_2"><i><font color="Green">E94</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:113_2_1_2_1"/>
( <font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> )
 </span><b>by </b><i><a class="txt" href="fsm_1.html#E6:113_2_1_2"><i><font color="Green">E95</font></i></a>, <a class="txt" href="fsm_1.html#E7:113_2_1_2"><i><font color="Green">E96</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_1_2_1_1"><b>suppose </b></a><a NAME="E1:113_2_1_2_1_1"/><i><font color="Green">E97</font></i>: 
<font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>17</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E12:113"><i><font color="Green">E89</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>21</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E6:113_2_1_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:113_2_1_2_1_1"/>
(  not <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> or  not <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>23</sub></font> )
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="ref" href="fsm_1.html#T78" target="_self">Th78</a></i>;<br/><b>hence </b><a NAME="E5:113_2_1_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_1"><i><font color="Green">E91</font></i></a>, <a class="txt" href="fsm_1.html#E6:113_2_1_2"><i><font color="Green">E95</font></i></a>, <a class="txt" href="fsm_1.html#E1:113_2_1_2_1_1"><i><font color="Green">E97</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_1_2_1_2"><b>suppose </b></a><a NAME="E1:113_2_1_2_1_2"/><i><font color="Green">E97</font></i>: 
<font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>20</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K6">}</a></span>;<br/><div><i><font color="Green">E98</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_1_2_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_1_2_1_2_1"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:113_2_1_2_1_2_1"/><i><font color="Green">E100</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> or <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>21</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_1_2_1_2_1_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon">c<sub>23</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font><b> such that </b><a NAME="E1:113_2_1_2_1_2_1_1"/><i><font color="Green">E101</font></i>: 
( <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>21</sub></font> )
 ;<br/>

<a NAME="E2:113_2_1_2_1_2_1_1"/>
<font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E10:113"><i><font color="Green">E88</font></i></a>, <a class="txt" href="fsm_1.html#E1:113_2_1_2_1_2_1_1"><i><font color="Green">E101</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/>
<b>hence </b><a NAME="E3:113_2_1_2_1_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_1_2_1_2_1"><i><font color="Green">E99</font></i></a>, <a class="txt" href="fsm_1.html#E1:113_2_1_2_1_2_1_1"><i><font color="Green">E101</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/>


</div><b>end;</b></div><b>reconsider </b><font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>17</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E12:113"><i><font color="Green">E89</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>21</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E6:113_2_1_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><a NAME="E5:113_2_1_2_1_2_1"/>
(  not <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> or  not <font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> or ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>23</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>24</sub></font> ) )
 <b>by </b><i><a class="txt" href="fsm_1.html#E4:113"><i><font color="Green">E84</font></i></a></i>;<br/><b>hence </b><a NAME="E6:113_2_1_2_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_1"><i><font color="Green">E91</font></i></a>, <a class="txt" href="fsm_1.html#E1:113_2_1_2_1_2"><i><font color="Green">E97</font></i></a>, <a class="txt" href="fsm_1.html#E2:113_2_1_2_1_2_1"><i><font color="Green">E100</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_1_2_1_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_1_2_1_2_2"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:113_2_1_2_1_2_2"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>20</sub></font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/><b>reconsider </b><font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>20</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K6">}</a></span> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/><b>consider </b><font color="Maroon">c<sub>25</sub></font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E6:113_2_1_2_1_2_2"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_1_2_1_2_2"><i><font color="Green">E99</font></i></a>, <a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/><a NAME="E7:113_2_1_2_1_2_2"/><i><font color="Green">E102</font></i>: 
<font color="Maroon">c<sub>24</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E7:113_2_1_2"><i><font color="Green">E96</font></i></a>, <a class="txt" href="fsm_1.html#E2:113_2_1_2_1_2_2"><i><font color="Green">E100</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_1_2_1_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:113_2_1_2_1_2_2_1"/>
( <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> )
 </span><b>by </b><i><a class="txt" href="fsm_1.html#E6:113_2_1_2_1_2_2"><i><font color="Green">E101</font></i></a>, <a class="txt" href="fsm_1.html#E7:113_2_1_2_1_2_2"><i><font color="Green">E102</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_1_2_1_2_2_1_1"><b>suppose </b></a><a NAME="E1:113_2_1_2_1_2_2_1_1"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><a NAME="E2:113_2_1_2_1_2_2_1_1"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E6:113_2_1_2_1_2_2"><i><font color="Green">E101</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>17</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E12:113"><i><font color="Green">E89</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>27</sub></font> = <font color="Maroon">c<sub>25</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E2:113_2_1_2_1_2_2_1_1"><i><font color="Green">E104</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><a NAME="E5:113_2_1_2_1_2_2_1_1"/>
(  not <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> or  not <font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>27</sub></font> )
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="ref" href="fsm_1.html#T78" target="_self">Th78</a></i>;<br/><b>hence </b><a NAME="E6:113_2_1_2_1_2_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_1"><i><font color="Green">E91</font></i></a>, <a class="txt" href="fsm_1.html#E1:113_2_1_2_1_2_2_1_1"><i><font color="Green">E103</font></i></a>, <a class="txt" href="fsm_1.html#E2:113_2_1_2_1_2_2_1_1"><i><font color="Green">E104</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_1_2_1_2_2_1_2"><b>suppose </b></a><a NAME="E1:113_2_1_2_1_2_2_1_2"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>21</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E6:113_2_1_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><a NAME="E3:113_2_1_2_1_2_2_1_2"/>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E6:113_2_1_2_1_2_2"><i><font color="Green">E101</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>27</sub></font> = <font color="Maroon">c<sub>25</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> <b>by </b><i><a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><a NAME="E5:113_2_1_2_1_2_2_1_2"/>
(  not <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> or  not <font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>27</sub></font> )
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="ref" href="fsm_1.html#T79" target="_self">Th79</a></i>;<br/><b>hence </b><a NAME="E6:113_2_1_2_1_2_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_1_2_1_2"><i><font color="Green">E97</font></i></a>, <a class="txt" href="fsm_1.html#E6:113_2_1_2_1_2_2"><i><font color="Green">E101</font></i></a>, <a class="txt" href="fsm_1.html#E1:113_2_1_2_1_2_2_1_2"><i><font color="Green">E103</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:113_2_1_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E2:113_2_1_2_1_2"><i><font color="Green">E98</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:113_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E2:113_2_1"><i><font color="Green">E92</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_2"><b>suppose </b></a><a NAME="E1:113_2_2"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>17</sub></font></span><a href="domain_1.html#K6">}</a></span>;<br/><div><i><font color="Green">E92</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_2_1"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>17</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>17</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_2"><i><font color="Green">E91</font></i></a></i>;<br/><a NAME="E3:113_2_2_1"/>
<font color="Maroon">c<sub>19</sub></font> is <a href="fsm_1.html#V6" target="_self">accessible</a>
 <b>by </b><i><a class="ref" href="fsm_1.html#D22" target="_self">Def22</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>20</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:113_2_2_1"/><i><font color="Green">E94</font></i>: 
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="fsm_1.html#R1" target="_self">-leads_to</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="ref" href="fsm_1.html#D21" target="_self">Def21</a></i>;<br/><b>set </b><font color="Maroon">c<sub>21</sub></font> = the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>4</sub></font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">c<sub>20</sub></font>;<br/><div><i><font color="Green">E95</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_2_1_1"/><i><font color="Green">E96</font></i>: 
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>4</sub></font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/><a NAME="E2:113_2_2_1_1"/>
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>4</sub></font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/><b>hence </b><a NAME="E3:113_2_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_2_1"><i><font color="Green">E93</font></i></a>, <a class="txt" href="fsm_1.html#E1:113_2_2_1_1"><i><font color="Green">E96</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_2_1_2"/><i><font color="Green">E96</font></i>: 
not the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>4</sub></font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/><a NAME="E2:113_2_2_1_2"/><i><font color="Green">E97</font></i>: 
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>4</sub></font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>19</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/><b>reconsider </b><font color="Maroon">c<sub>23</sub></font> = the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>4</sub></font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">c<sub>20</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="txt" href="fsm_1.html#E2:113_2_2_1_2"><i><font color="Green">E97</font></i></a>, <a class="ref" href="fsm_1.html#D24" target="_self">Def24</a></i>;<br/><a NAME="E5:113_2_2_1_2"/><i><font color="Green">E98</font></i>: 
 <a href="fsm_1.html#K8" target="_self">final_states_partition</a> <font color="Maroon">c<sub>3</sub></font> is <a href="fsm_1.html#V4" target="_self">final</a>
 <b>by </b><i><a class="ref" href="fsm_1.html#D15" target="_self">Def15</a></i>;<br/><a NAME="E6:113_2_2_1_2"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> holds <br/>(  not <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> or  not <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_2_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:113_2_2_1_2_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> )
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>24</sub></font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">c<sub>3</sub></font></span>)</span><b> such that </b><br/><a NAME="E3:113_2_2_1_2_1"/><i><font color="Green">E99</font></i>: 
( <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font> )
 ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>24</sub></font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E6:113"><i><font color="Green">E86</font></i></a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E5:113_2_2_1_2_1"/>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
;<br/>
<a NAME="E6:113_2_2_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a>  <a href="fsm_1.html#K8" target="_self">final_states_partition</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="fsm_1.html#D18" target="_self">Def18</a></i>;<br/>
<a NAME="E7:113_2_2_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>25</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E9:113"><i><font color="Green">E87</font></i></a>, <a class="txt" href="fsm_1.html#E1:113_2_2_1_2"><i><font color="Green">E96</font></i></a>, <a class="txt" href="fsm_1.html#E3:113_2_2_1_2_1"><i><font color="Green">E99</font></i></a>, <a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E8:113_2_2_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E12:113"><i><font color="Green">E89</font></i></a>, <a class="txt" href="fsm_1.html#E3:113_2_2_1_2_1"><i><font color="Green">E99</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>


</div><b>end;</b></div><a NAME="E7:113_2_2_1_2"/><b>then </b>
not <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="fsm_1.html#R5" target="_self">-are_equivalent</a> 
 <b>by </b><i><a class="txt" href="fsm_1.html#E6:113"><i><font color="Green">E86</font></i></a>, <a class="txt" href="fsm_1.html#E5:113_2_2_1_2"><i><font color="Green">E98</font></i></a>, <a class="ref" href="fsm_1.html#D14" target="_self">Def14</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>24</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E9:113_2_2_1_2"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i><a class="ref" href="fsm_1.html#D10" target="_self">Def10</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>23</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> ;<br/><b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>22</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> ;<br/><a NAME="E12:113_2_2_1_2"/><i><font color="Green">E100</font></i>: 
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="fsm_1.html#R1" target="_self">-leads_to</a> <font color="Maroon">c<sub>25</sub></font>
 <b>by </b><i><a class="ref" href="fsm_1.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E13:113_2_2_1_2"/>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="ref" href="fsm_1.html#T74" target="_self">Th74</a></i>;<br/><a NAME="E14:113_2_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="txt" href="fsm_1.html#E9:113_2_2_1_2"><i><font color="Green">E99</font></i></a>, <a class="ref" href="fsm_1.html#T72" target="_self">Th72</a></i>;<br/><a NAME="E15:113_2_2_1_2"/><b>then </b>
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i><a class="txt" href="fsm_1.html#E5:113_2_2_1"><i><font color="Green">E94</font></i></a>, <a class="txt" href="fsm_1.html#E12:113_2_2_1_2"><i><font color="Green">E100</font></i></a>, <a class="ref" href="fsm_1.html#T27" target="_self">Th27</a></i>;<br/><b>hence </b><a NAME="E16:113_2_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="ref" href="fsm_1.html#D9" target="_self">Def9</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:113_2_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E6:113_2_2_1"><i><font color="Green">E95</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_2_2"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>17</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:113_2_2_2"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>17</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>16</sub></font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/><b>reconsider </b><font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>17</sub></font></span><a href="domain_1.html#K6">}</a></span> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/><b>consider </b><font color="Maroon">c<sub>21</sub></font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E6:113_2_2_2"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_2_2"><i><font color="Green">E93</font></i></a>, <a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/><a NAME="E7:113_2_2_2"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E14:113"><i><font color="Green">E90</font></i></a>, <a class="txt" href="fsm_1.html#E2:113_2_2_2"><i><font color="Green">E94</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:113_2_2_2_1"/>
( <font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> )
 </span><b>by </b><i><a class="txt" href="fsm_1.html#E6:113_2_2_2"><i><font color="Green">E95</font></i></a>, <a class="txt" href="fsm_1.html#E7:113_2_2_2"><i><font color="Green">E96</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_2_2_1_1"><b>suppose </b></a><a NAME="E1:113_2_2_2_1_1"/><i><font color="Green">E97</font></i>: 
<font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>20</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K6">}</a></span>;<br/><div><i><font color="Green">E98</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_2_2_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_2_2_1_1_1"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:113_2_2_2_1_1_1"/><i><font color="Green">E100</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> or <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>21</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_2_2_1_1_1_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon">c<sub>23</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font><b> such that </b><a NAME="E1:113_2_2_2_1_1_1_1"/><i><font color="Green">E101</font></i>: 
( <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>21</sub></font> )
 ;<br/>

<a NAME="E2:113_2_2_2_1_1_1_1"/>
<font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E10:113"><i><font color="Green">E88</font></i></a>, <a class="txt" href="fsm_1.html#E1:113_2_2_2_1_1_1_1"><i><font color="Green">E101</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/>
<b>hence </b><a NAME="E3:113_2_2_2_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_2_2_1_1_1"><i><font color="Green">E99</font></i></a>, <a class="txt" href="fsm_1.html#E1:113_2_2_2_1_1_1_1"><i><font color="Green">E101</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/>


</div><b>end;</b></div><b>reconsider </b><font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>17</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E12:113"><i><font color="Green">E89</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>21</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E6:113_2_2_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><a NAME="E5:113_2_2_2_1_1_1"/>
(  not <font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> or  not <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> or ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>24</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>23</sub></font> ) )
 <b>by </b><i><a class="txt" href="fsm_1.html#E4:113"><i><font color="Green">E84</font></i></a></i>;<br/><b>hence </b><a NAME="E6:113_2_2_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_2"><i><font color="Green">E91</font></i></a>, <a class="txt" href="fsm_1.html#E1:113_2_2_2_1_1"><i><font color="Green">E97</font></i></a>, <a class="txt" href="fsm_1.html#E2:113_2_2_2_1_1_1"><i><font color="Green">E100</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_2_2_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_2_2_1_1_2"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:113_2_2_2_1_1_2"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>20</sub></font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/><b>reconsider </b><font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>20</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K6">}</a></span> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/><b>consider </b><font color="Maroon">c<sub>25</sub></font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E6:113_2_2_2_1_1_2"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_2_2_1_1_2"><i><font color="Green">E99</font></i></a>, <a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/><a NAME="E7:113_2_2_2_1_1_2"/><i><font color="Green">E102</font></i>: 
<font color="Maroon">c<sub>24</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E7:113_2_2_2"><i><font color="Green">E96</font></i></a>, <a class="txt" href="fsm_1.html#E2:113_2_2_2_1_1_2"><i><font color="Green">E100</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_2_2_1_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:113_2_2_2_1_1_2_1"/>
( <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> )
 </span><b>by </b><i><a class="txt" href="fsm_1.html#E6:113_2_2_2_1_1_2"><i><font color="Green">E101</font></i></a>, <a class="txt" href="fsm_1.html#E7:113_2_2_2_1_1_2"><i><font color="Green">E102</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_2_2_1_1_2_1_1"><b>suppose </b></a><a NAME="E1:113_2_2_2_1_1_2_1_1"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>21</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E6:113_2_2_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><a NAME="E3:113_2_2_2_1_1_2_1_1"/>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E6:113_2_2_2_1_1_2"><i><font color="Green">E101</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>27</sub></font> = <font color="Maroon">c<sub>25</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> <b>by </b><i><a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><a NAME="E5:113_2_2_2_1_1_2_1_1"/>
(  not <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> or  not <font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>27</sub></font> )
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="ref" href="fsm_1.html#T78" target="_self">Th78</a></i>;<br/><b>hence </b><a NAME="E6:113_2_2_2_1_1_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_2_2_1_1"><i><font color="Green">E97</font></i></a>, <a class="txt" href="fsm_1.html#E6:113_2_2_2_1_1_2"><i><font color="Green">E101</font></i></a>, <a class="txt" href="fsm_1.html#E1:113_2_2_2_1_1_2_1_1"><i><font color="Green">E103</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_2_2_1_1_2_1_2"><b>suppose </b></a><a NAME="E1:113_2_2_2_1_1_2_1_2"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 ;<br/><div class="add"><a NAME="E2:113_2_2_2_1_1_2_1_2"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E6:113_2_2_2_1_1_2"><i><font color="Green">E101</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>17</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E12:113"><i><font color="Green">E89</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>27</sub></font> = <font color="Maroon">c<sub>25</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E2:113_2_2_2_1_1_2_1_2"><i><font color="Green">E104</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><a NAME="E5:113_2_2_2_1_1_2_1_2"/>
(  not <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> or  not <font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>27</sub></font> )
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="ref" href="fsm_1.html#T79" target="_self">Th79</a></i>;<br/><b>hence </b><a NAME="E6:113_2_2_2_1_1_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_2"><i><font color="Green">E91</font></i></a>, <a class="txt" href="fsm_1.html#E1:113_2_2_2_1_1_2_1_2"><i><font color="Green">E103</font></i></a>, <a class="txt" href="fsm_1.html#E2:113_2_2_2_1_1_2_1_2"><i><font color="Green">E104</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:113_2_2_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E2:113_2_2_2_1_1"><i><font color="Green">E98</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_2_2_1_2"><b>suppose </b></a><a NAME="E1:113_2_2_2_1_2"/><i><font color="Green">E97</font></i>: 
<font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>17</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E12:113"><i><font color="Green">E89</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>21</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>19</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E6:113_2_2_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:113_2_2_2_1_2"/>
(  not <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> or  not <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>23</sub></font> )
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="ref" href="fsm_1.html#T79" target="_self">Th79</a></i>;<br/><b>hence </b><a NAME="E5:113_2_2_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_2"><i><font color="Green">E91</font></i></a>, <a class="txt" href="fsm_1.html#E6:113_2_2_2"><i><font color="Green">E95</font></i></a>, <a class="txt" href="fsm_1.html#E1:113_2_2_2_1_2"><i><font color="Green">E97</font></i></a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:113_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E2:113_2_2"><i><font color="Green">E92</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
