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

<a NAME="E1:15_1_1"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
<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_2.html#K3" title="FINSEQ_2:func.3">*</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_2.html#K3" title="FINSEQ_2:func.3">*</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T15" title="FUNCT_4:th.15">FUNCT_4:15</a></span>;<br/>
<a NAME="E2:15_1_1"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
 <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_2.html#K3" title="FINSEQ_2:func.3">*</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_2.html#K3" title="FINSEQ_2:func.3">*</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="15_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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_2.html#K3" title="FINSEQ_2:func.3">*</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_2.html#K3" title="FINSEQ_2:func.3">*</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/>

<span class="lab"><font color="Green" title="E7">A3</font></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="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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></span>
;<br/>
<span class="kw">assume </span><a NAME="E2:15_1_1_1"/>
<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_2.html#K3" title="FINSEQ_2:func.3">*</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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_2.html#K3" title="FINSEQ_2:func.3">*</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/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E4:15_1_1_1"/><span class="lab"><font color="Green" title="E8">A4</font></span>: 
<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_2.html#K3" title="FINSEQ_2:func.3">*</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="kw">and </span><br/><a NAME="E5:15_1_1_1"/><span class="lab"><font color="Green" title="E9">A5</font></span>: 
<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_2.html#K3" title="FINSEQ_2:func.3">*</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<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"><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_2.html#K3" title="FINSEQ_2:func.3">*</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_2.html#K3" title="FINSEQ_2:func.3">*</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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1_1"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>
<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_2.html#K3" title="FINSEQ_2:func.3">*</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></span>
;<br/>
<a NAME="E7:15_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A6</font></span>: 
( <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_2.html#K3" title="FINSEQ_2:func.3">*</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> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:15_1_1_1"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1_1_3"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:15_1_1_1_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_2.html#K3" title="FINSEQ_2:func.3">*</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><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1_1_1"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E7:15_1_1_1"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1_1_3_1"><span class="kw">suppose </span></a><a NAME="E1:15_1_1_1_3_1"/><span class="lab"><font color="Green" title="E11">A7</font></span>: 
<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_2.html#K3" title="FINSEQ_2:func.3">*</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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_2.html#K3" title="FINSEQ_2:func.3">*</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="E2:15_1_1_1_3_1"/><span class="kw">then </span>
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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E3:15_1_1_1_3_1"/><span class="kw">then </span>
<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_2.html#K3" title="FINSEQ_2:func.3">*</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1_1"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="txt" href="#E5:15_1_1_1"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>;<br/><a NAME="E4:15_1_1_1_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A8</font></span>: 
<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_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1_1_1_3_1"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/><a NAME="E5:15_1_1_1_3_1"/>
( <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_2.html#K3" title="FINSEQ_2:func.3">*</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_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp;  <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_2.html#K3" title="FINSEQ_2:func.3">*</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_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a>, <a class="ref" href="zfmisc_1.html#T12" title="ZFMISC_1:th.12">ZFMISC_1:12</a></span>;<br/><a NAME="E6:15_1_1_1_3_1"/><span class="kw">then </span>
 <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_2.html#K3" title="FINSEQ_2:func.3">*</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_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><span class="kw">hence </span><a NAME="E7:15_1_1_1_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_2.html#K3" title="FINSEQ_2:func.3">*</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E4:15_1_1_1_3_1"><span class="lab"><font color="Green" title="E12">A8</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1_1_3_2"><span class="kw">suppose </span></a><a NAME="E1:15_1_1_1_3_2"/><span class="lab"><font color="Green" title="E11">A9</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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_2.html#K3" title="FINSEQ_2:func.3">*</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="E2:15_1_1_1_3_2"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15_1_1_1"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>;<br/><a NAME="E3:15_1_1_1_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A10</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1_1_1_3_2"><span class="lab"><font color="Green" title="E11">A9</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/><a NAME="E4:15_1_1_1_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T45" title="RELAT_1:th.45">RELAT_1:45</a></span>;<br/><a NAME="E5:15_1_1_1_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A11</font></span>: 
 <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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T14" title="FUNCOP_1:th.14">FUNCOP_1:14</a></span>;<br/><a NAME="E6:15_1_1_1_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T12" title="ZFMISC_1:th.12">ZFMISC_1:12</a></span>;<br/><a NAME="E7:15_1_1_1_3_2"/><span class="kw">then </span>
 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15_1_1_1_3_2"><span class="lab"><font color="Green" title="E13">A11</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><span class="kw">hence </span><a NAME="E8:15_1_1_1_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_2.html#K3" title="FINSEQ_2:func.3">*</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15_1_1_1_3_2"><span class="lab"><font color="Green" title="E12">A10</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1_1_3_3"><span class="kw">suppose </span></a><a NAME="E1:15_1_1_1_3_3"/><span class="lab"><font color="Green" title="E11">A12</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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_2.html#K3" title="FINSEQ_2:func.3">*</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="E2:15_1_1_1_3_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A13</font></span>: 
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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E3:15_1_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> <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1_1_1_3_3"><span class="lab"><font color="Green" title="E11">A12</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><a NAME="E4:15_1_1_1_3_3"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A14</font></span>: <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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1_1"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="txt" href="#E5:15_1_1_1"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15_1_1_1_3_3"><span class="lab"><font color="Green" title="E12">A13</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>
;<br/><a NAME="E6:15_1_1_1_3_3"/>
<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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1_1_1_3_3"><span class="lab"><font color="Green" title="E11">A12</font></span></a></span>;<br/><a NAME="E7:15_1_1_1_3_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A15</font></span>: 
<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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><a NAME="E8:15_1_1_1_3_3"/><span class="lab"><font color="Green" title="E15">A16</font></span>: 
 <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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><a NAME="E9:15_1_1_1_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="15_1_1_1_3_3_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E1:15_1_1_1_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">u</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:15_1_1_1_3_3_2"/><span class="lab"><font color="Green" title="E16">A17</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E4:15_1_1_1_3_3_2"/><span class="lab"><font color="Green" title="E17">A18</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<a NAME="E5:15_1_1_1_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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T87" title="RELAT_1:th.87">RELAT_1:87</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15_1_1_1_3_3_2"><span class="lab"><font color="Green" title="E16">A17</font></span></a></span>;<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15_1_1_1_3_3_2"><span class="lab"><font color="Green" title="E16">A17</font></span></a>, <a class="txt" href="#E4:15_1_1_1_3_3_2"><span class="lab"><font color="Green" title="E17">A18</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>
<br/>.= 
 <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#T11" title="AMI_2:th.11">AMI_2:11</a></span>
;<br/>
<a NAME="E8:15_1_1_1_3_3_2"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:15_1_1_1_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span> <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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T46" title="RELAT_1:th.46">RELAT_1:46</a></span>
<br/>.= 
 <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:15_1_1_1_3_3"><span class="lab"><font color="Green" title="E15">A16</font></span></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></span>
;<br/><a NAME="E11:15_1_1_1_3_3"/><span class="kw">then </span>
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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1_1_1_3_3"><span class="lab"><font color="Green" title="E11">A12</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E12:15_1_1_1_3_3"/><span class="kw">then </span>
<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"><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="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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15_1_1_1_3_3"><span class="lab"><font color="Green" title="E14">A15</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><a NAME="E13:15_1_1_1_3_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A19</font></span>: 
( <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"><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> 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 class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1_1_3_3_4"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1_1_3_3_4_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:15_1_1_1_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><span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:15_1_1_1_3_3"><span class="lab"><font color="Green" title="E16">A19</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1_1_3_3_4_1_1"><span class="kw">suppose </span></a><a NAME="E1:15_1_1_1_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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_2.html#K3" title="FINSEQ_2:func.3">*</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="E2:15_1_1_1_3_3_4_1_1"/><span class="kw">then </span>
<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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15_1_1_1_3_3"><span class="lab"><font color="Green" title="E13">A14</font></span></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></span>;<br/><a NAME="E3:15_1_1_1_3_3_4_1_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E4:15_1_1_1_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_2.html#K3" title="FINSEQ_2:func.3">*</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 class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1_1_3_3_4_1_2"><span class="kw">suppose </span></a><a NAME="E1:15_1_1_1_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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_2.html#K3" title="FINSEQ_2:func.3">*</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="E2:15_1_1_1_3_3_4_1_2"/><span class="kw">then </span>
<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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15_1_1_1_3_3"><span class="lab"><font color="Green" title="E13">A14</font></span></a>, <a class="ref" href="ami_2.html#T10" title="AMI_2:th.10">AMI_2:10</a></span>;<br/><a NAME="E3:15_1_1_1_3_3_4_1_2"/><span class="kw">then </span>
<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_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E4:15_1_1_1_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_2.html#K3" title="FINSEQ_2:func.3">*</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 class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E15:15_1_1_1_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_2.html#K3" title="FINSEQ_2:func.3">*</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<a NAME="E3:15_1_1"/><span class="lab"><font color="Green" title="E7">A20</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T44" title="RELAT_1:th.44">RELAT_1:44</a></span>;<br/>
<a NAME="E4:15_1_1"/>
(  <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>  &amp;  <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>  )
 
<span class="kw">by</span> <span class="lab"><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>, <a class="ref" href="relat_1.html#T89" title="RELAT_1:th.89">RELAT_1:89</a></span>;<br/>
<a NAME="E5:15_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E8">A21</font></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> <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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<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_2.html#K3" title="FINSEQ_2:func.3">*</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_2.html#K3" title="FINSEQ_2:func.3">*</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>
<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> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>
<br/>.= 
 <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> 
<span class="kw">by</span> <span class="lab"><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></span>
;<br/>
<span class="kw">then </span> <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_2.html#K3" title="FINSEQ_2:func.3">*</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>
<br/>.= 
 <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15_1_1"><span class="lab"><font color="Green" title="E8">A21</font></span></a>, <a class="txt" href="#E3:15_1_1"><span class="lab"><font color="Green" title="E7">A20</font></span></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></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:15_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_2.html#K3" title="FINSEQ_2:func.3">*</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">(<span class="default"><span class="p2"><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="p3">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</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="p2"><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>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15_1_1"><span class="lab"><font color="Green" title="E6">A2</font></span></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></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
