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

<b>let </b><font color="Maroon" title="c1">la</font> be    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not  <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">goto</a> <font color="Maroon" title="c1">la</font> is <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a></span><br/>

<b>assume </b><a NAME="E1:82"/><i><font color="Green" title="E61">A1</font></i>: 
 <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">goto</a> <font color="Maroon" title="c1">la</font> is <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>reconsider </b><font color="Maroon" title="c2">a3</font> = <font color="Maroon" title="c1">la</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c3">s</font> being   <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a>;<br/>
<b>set </b><font color="Maroon" title="c4">t</font> = <font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c5">f</font> = the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>
<b>consider </b><font color="Maroon" title="c6">mj</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> ;<br/>
<b>consider </b><font color="Maroon" title="c7">L</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> ;<br/>
<a NAME="E6:82"/><i><font color="Green" title="E62">A2</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E7:82"/><b>then </b>
 <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>then </b><i><font color="Green" title="E63">A3</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  = 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
<b>by </b><i><a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/>
<a NAME="E9:82"/><i><font color="Green" title="E64">A4</font></i>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> 
 
<b>by </b><i><a class="ref" href="scmfsa_1.html#T5" title="SCMFSA_1:th.5">SCMFSA_1:5</a>, <a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E10:82"/><i><font color="Green" title="E65">A5</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="scmfsa_1.html#K7" title="SCMFSA_1:func.7">SCM+FSA-OK</a> 
 
<b>by </b><i><a class="ref" href="card_3.html#T18" title="CARD_3:th.18">CARD_3:18</a></i>;<br/>
<i><font color="Green" title="E66">A6</font></i>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>
<br/>.= 
<a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E10:82"><i><font color="Green" title="E65">A5</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>
<br/>.= 
<a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>
<br/>.= 
 <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E9:82"><i><font color="Green" title="E64">A4</font></i></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>
;<br/>
<a NAME="E12:82"/><i><font color="Green" title="E67">A7</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E13:82"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="82_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> )</span><br/>

<b>assume </b><a NAME="E1:82_3"/><i><font color="Green" title="E68">A8</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:82_3_1"/>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  or <font color="Maroon" title="c8">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_3_1_1"><b>suppose </b></a><a NAME="E1:82_3_1_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span><br/><div class="add"><b>hence </b><a NAME="E2:82_3_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E8:82"><i><font color="Green" title="E63">A3</font></i></a>, <a class="ref" href="scmfsa_1.html#T9" title="SCMFSA_1:th.9">SCMFSA_1:9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_3_1_2"><b>suppose </b></a><a NAME="E1:82_3_1_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span><br/><div class="add"><a NAME="E2:82_3_1_2"/><b>then </b>
not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E6:82"><i><font color="Green" title="E62">A2</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:82_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
 <b>by </b><i><a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>;<br/><b>hence </b><a NAME="E4:82_3_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E1:82_3"><i><font color="Green" title="E68">A8</font></i></a>, <a class="ref" href="card_3.html#T18" title="CARD_3:th.18">CARD_3:18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c8">t</font> = <font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <font color="Maroon" title="c2">a3</font></span>)</span></span>)</span> as   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <b>by </b><i><a class="txt" href="scmfsa_2.html#E11:82"><i><font color="Green" title="E66">A6</font></i></a>, <a class="txt" href="scmfsa_2.html#E12:82"><i><font color="Green" title="E67">A7</font></i></a>, <a class="ref" href="card_3.html#T18" title="CARD_3:th.18">CARD_3:18</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">w</font> = <font color="Maroon" title="c8">t</font> as   <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> ;<br/>
<a NAME="E16:82"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c1">la</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E17:82"/><b>then </b>
 <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c1">la</font></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>then </b><i><font color="Green" title="E68">A9</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c9">w</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c1">la</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  = 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c1">la</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
<b>by </b><i><a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon" title="c1">la</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">w</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c1">la</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  = 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <font color="Maroon" title="c9">w</font>,<font color="Maroon" title="c2">a3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 

<br/>.= 
<font color="Maroon" title="c2">a3</font>
<b>by </b><i><a class="ref" href="scmfsa_1.html#T20" title="SCMFSA_1:th.20">SCMFSA_1:20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">goto</a> <font color="Maroon" title="c1">la</font></span>)</span>,<font color="Maroon" title="c8">t</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T7" target="_self" title="SCMFSA_2:th.7">Th7</a>, <a class="ref" href="scmfsa_2.html#T95" target="_self" title="SCMFSA_2:th.95">Th95</a></i>
<br/>.= 
<font color="Maroon" title="c8">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E1:82"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a></i>
;<br/>
<b>hence </b><a NAME="E20:82"/>
contradiction
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E8:82"><i><font color="Green" title="E63">A3</font></i></a>, <a class="txt" href="scmfsa_2.html#E18:82"><i><font color="Green" title="E68">A9</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
