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

<a NAME="E1:14_1_1"/><i><font color="Green" title="E4">A1</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <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#T1" target="_self" title="SCMFSA_1:th.1">Th1</a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E2:14_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T89" title="RELAT_1:th.89">RELAT_1:89</a></i>;<br/>
<a NAME="E3:14_1_1"/><b>then </b><i><font color="Green" title="E5">A2</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</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="txt" href="scmfsa_1.html#E1:14_1_1"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:14_1_1"/><i><font color="Green" title="E6">A3</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T44" title="RELAT_1:th.44">RELAT_1:44</a></i>;<br/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </span>)</span> = 
<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#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span></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> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </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> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </span>)</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>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="ami_2.html#K3" title="AMI_2:func.3">SCM-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 href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E7">A4</font></i>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p4">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span> = 
<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"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </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> 
<b>by </b><i><a class="txt" href="scmfsa_1.html#E3:14_1_1"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="scmfsa_1.html#E4:14_1_1"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>
;<br/>
<a NAME="E7:14_1_1"/><i><font color="Green" title="E8">A5</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T15" title="FUNCT_4:th.15">FUNCT_4:15</a></i>;<br/>
<a NAME="E8:14_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p4">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c1">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p4">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span> or <font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )</span><br/>

<b>assume </b><a NAME="E1:14_1_1_3"/>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p4">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><br/>

<b>then consider </b><font color="Maroon" title="c2">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:14_1_1_3"/><i><font color="Green" title="E9">A6</font></i>: 
<font color="Maroon" title="c2">z</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p4">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:14_1_1_3"/><i><font color="Green" title="E10">A7</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p4">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">y</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<i><font color="Green" title="E11">A8</font></i>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p4">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </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> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span></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="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p4">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_1.html#E7:14_1_1"><i><font color="Green" title="E8">A5</font></i></a>, <a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p4">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p5">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span></span>)</span></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="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p4">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></i>
;<br/>
<i><font color="Green" title="E12">A9</font></i>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </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> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </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"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </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/>.= 
<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"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p4">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></i>
;<br/>
<a NAME="E7:14_1_1_3"/><i><font color="Green" title="E13">A10</font></i>: 
( <font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</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="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p4">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span></span>)</span> or <font color="Maroon" title="c2">z</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="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="scmfsa_1.html#E3:14_1_1_3"><i><font color="Green" title="E9">A6</font></i></a>, <a class="txt" href="scmfsa_1.html#E5:14_1_1_3"><i><font color="Green" title="E11">A8</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_3_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:14_1_1_3_3"/>
( <font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</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="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p4">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span></span>)</span> or <font color="Maroon" title="c2">z</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"><span class="p2">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span> or <font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</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"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span> )
 </span><b>by </b><i><a class="txt" href="scmfsa_1.html#E6:14_1_1_3"><i><font color="Green" title="E12">A9</font></i></a>, <a class="txt" href="scmfsa_1.html#E7:14_1_1_3"><i><font color="Green" title="E13">A10</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_3_3_1"><b>suppose </b></a><a NAME="E1:14_1_1_3_3_1"/><i><font color="Green" title="E14">A11</font></i>: 
<font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</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="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p4">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><br/><div class="add"><a NAME="E2:14_1_1_3_3_1"/><b>then </b>
not <font color="Maroon" title="c2">z</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="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E3:14_1_1_3_3_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">y</font>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E7:14_1_1"><i><font color="Green" title="E8">A5</font></i></a>, <a class="txt" href="scmfsa_1.html#E4:14_1_1_3"><i><font color="Green" title="E10">A7</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>;<br/><a NAME="E4:14_1_1_3_3_1"/><b>then </b><i><font color="Green" title="E15">A12</font></i>: 
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E1:14_1_1_3_3_1"><i><font color="Green" title="E14">A11</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><a NAME="E5:14_1_1_3_3_1"/><i><font color="Green" title="E16">A13</font></i>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T12" title="ZFMISC_1:th.12">ZFMISC_1:12</a></i>;<br/><a NAME="E6:14_1_1_3_3_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></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="E7:14_1_1_3_3_1"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E5:14_1_1_3_3_1"><i><font color="Green" title="E16">A13</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><b>hence </b><a NAME="E8:14_1_1_3_3_1"/>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E4:14_1_1_3_3_1"><i><font color="Green" title="E15">A12</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</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="14_1_1_3_3_2"><b>suppose </b></a><a NAME="E1:14_1_1_3_3_2"/><i><font color="Green" title="E14">A14</font></i>: 
<font color="Maroon" title="c2">z</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"><span class="p2">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><br/><div class="add"><a NAME="E2:14_1_1_3_3_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">y</font>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E4:14_1_1_3"><i><font color="Green" title="E10">A7</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>;<br/><a NAME="E3:14_1_1_3_3_2"/><b>then </b><i><font color="Green" title="E15">A15</font></i>: 
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E1:14_1_1_3_3_2"><i><font color="Green" title="E14">A14</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><a NAME="E4:14_1_1_3_3_2"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T45" title="RELAT_1:th.45">RELAT_1:45</a></i>;<br/><a NAME="E5:14_1_1_3_3_2"/><b>then </b><i><font color="Green" title="E16">A16</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T14" title="FUNCOP_1:th.14">FUNCOP_1:14</a></i>;<br/><a NAME="E6:14_1_1_3_3_2"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T12" title="ZFMISC_1:th.12">ZFMISC_1:12</a></i>;<br/><a NAME="E7:14_1_1_3_3_2"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E5:14_1_1_3_3_2"><i><font color="Green" title="E16">A16</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><b>hence </b><a NAME="E8:14_1_1_3_3_2"/>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E3:14_1_1_3_3_2"><i><font color="Green" title="E15">A15</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</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="14_1_1_3_3_3"><b>suppose </b></a><a NAME="E1:14_1_1_3_3_3"/><i><font color="Green" title="E14">A17</font></i>: 
<font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</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"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><br/><div class="add"><a NAME="E2:14_1_1_3_3_3"/><b>then </b><i><font color="Green" title="E15">A18</font></i>: 
not <font color="Maroon" title="c2">z</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"><span class="p2">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E3:14_1_1_3_3_3"/><i><font color="Green" title="E16">A19</font></i>: 
<font color="Maroon" title="c2">z</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> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> 
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E1:14_1_1_3_3_3"><i><font color="Green" title="E14">A17</font></i></a></i>;<br/><a NAME="E4:14_1_1_3_3_3"/>
<font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </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"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E1:14_1_1_3_3_3"><i><font color="Green" title="E14">A17</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E5:14_1_1_3_3_3"/><b>then </b>
<font color="Maroon" title="c2">z</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="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </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/><b>then </b><i><font color="Green" title="E17">A20</font></i>: <font color="Maroon" title="c1">y</font> = 
<span class="p1">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">z</font>
<b>by </b><i><a class="txt" href="scmfsa_1.html#E7:14_1_1"><i><font color="Green" title="E8">A5</font></i></a>, <a class="txt" href="scmfsa_1.html#E4:14_1_1_3"><i><font color="Green" title="E10">A7</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">z</font>
<b>by </b><i><a class="txt" href="scmfsa_1.html#E2:14_1_1_3_3_3"><i><font color="Green" title="E15">A18</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
;<br/><a NAME="E7:14_1_1_3_3_3"/><i><font color="Green" title="E18">A21</font></i>: 
<font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K3" title="AMI_2:func.3">SCM-Memory</a> 
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E3:14_1_1_3_3_3"><i><font color="Green" title="E16">A19</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><a NAME="E8:14_1_1_3_3_3"/><i><font color="Green" title="E19">A22</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K3" title="AMI_2:func.3">SCM-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="E9:14_1_1_3_3_3"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_3_3_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span> or <font color="Maroon" title="c3">e</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="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:14_1_1_3_3_3_2"/>
<font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">e</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="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span></span><br/>

<b>then consider </b><font color="Maroon" title="c4">u</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:14_1_1_3_3_3_2"/><i><font color="Green" title="E20">A23</font></i>: 
<font color="Maroon" title="c4">u</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="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span>
 <b>and </b><br/><a NAME="E4:14_1_1_3_3_3_2"/><i><font color="Green" title="E21">A24</font></i>: 
<span class="p1">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">e</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E5:14_1_1_3_3_3_2"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T87" title="RELAT_1:th.87">RELAT_1:87</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">u</font> = <font color="Maroon" title="c4">u</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="txt" href="scmfsa_1.html#E3:14_1_1_3_3_3_2"><i><font color="Green" title="E20">A23</font></i></a></i>;<br/>
<font color="Maroon" title="c3">e</font> = 
<a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">u</font>
<b>by </b><i><a class="txt" href="scmfsa_1.html#E3:14_1_1_3_3_3_2"><i><font color="Green" title="E20">A23</font></i></a>, <a class="txt" href="scmfsa_1.html#E4:14_1_1_3_3_3_2"><i><font color="Green" title="E21">A24</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>
<br/>.= 
 <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a> 
<b>by </b><i><a class="ref" href="ami_2.html#T11" title="AMI_2:th.11">AMI_2:11</a></i>
;<br/>
<a NAME="E8:14_1_1_3_3_3_2"/><b>then </b>
<font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E9:14_1_1_3_3_3_2"/>
<font color="Maroon" title="c3">e</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="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</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><b>then </b> <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span> = 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T46" title="RELAT_1:th.46">RELAT_1:46</a></i>
<br/>.= 
 <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
<b>by </b><i><a class="txt" href="scmfsa_1.html#E8:14_1_1_3_3_3"><i><font color="Green" title="E19">A22</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>
;<br/><a NAME="E11:14_1_1_3_3_3"/><b>then </b>
not <font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E1:14_1_1_3_3_3"><i><font color="Green" title="E14">A17</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E12:14_1_1_3_3_3"/><b>then </b>
<font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E7:14_1_1_3_3_3"><i><font color="Green" title="E18">A21</font></i></a>, <a class="ref" href="ami_3.html#D1" title="AMI_3:def.1">AMI_3:def 1</a>, <a class="ref" href="ami_5.html#T23" title="AMI_5:th.23">AMI_5:23</a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E13:14_1_1_3_3_3"/><b>then </b><i><font color="Green" title="E20">A25</font></i>: 
( <font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or <font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  )
 <b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_3_3_4"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_3_3_3_4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:14_1_1_3_3_3_4_1"/>
( <font color="Maroon" title="c2">z</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="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  )
 </span><b>by </b><i><a class="txt" href="scmfsa_1.html#E13:14_1_1_3_3_3"><i><font color="Green" title="E20">A25</font></i></a>, <a class="ref" href="ami_3.html#T4" title="AMI_3:th.4">AMI_3:4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_3_3_3_4_1_1"><b>suppose </b></a><a NAME="E1:14_1_1_3_3_3_4_1_1"/>
<font color="Maroon" title="c2">z</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"> <font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><br/><div class="add"><a NAME="E2:14_1_1_3_3_3_4_1_1"/><b>then </b>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E6:14_1_1_3_3_3"><i><font color="Green" title="E17">A20</font></i></a>, <a class="ref" href="ami_2.html#T7" title="AMI_2:th.7">AMI_2:7</a>, <a class="ref" href="ami_2.html#T30" title="AMI_2:th.30">AMI_2:30</a></i>;<br/><a NAME="E3:14_1_1_3_3_3_4_1_1"/><b>then </b>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E4:14_1_1_3_3_3_4_1_1"/>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</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="14_1_1_3_3_3_4_1_2"><b>suppose </b></a><a NAME="E1:14_1_1_3_3_3_4_1_2"/>
<font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><br/><div class="add"><a NAME="E2:14_1_1_3_3_3_4_1_2"/><b>then </b>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E6:14_1_1_3_3_3"><i><font color="Green" title="E17">A20</font></i></a>, <a class="ref" href="ami_2.html#T10" title="AMI_2:th.10">AMI_2:10</a></i>;<br/><a NAME="E3:14_1_1_3_3_3_4_1_2"/><b>then </b>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E4:14_1_1_3_3_3_4_1_2"/>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</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>hence </b><a NAME="E15:14_1_1_3_3_3"/>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ; <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>hence </b><a NAME="E9:14_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span>)</span> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> ,<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> ,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E6:14_1_1"><i><font color="Green" title="E7">A4</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</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>
