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

<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">i</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <br/> for <font color="Olive" title="b2">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>   st <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Olive" title="b1">i</font></span>)</span> holds <br/>for <font color="Olive" title="b3">s</font> being  <a href="scmnorm.html#NM1" title="SCMNORM:NM.1">preProgram</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds   <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Olive" title="b3">s</font></span>)</span>,<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Olive" title="b1">i</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Olive" title="b3">s</font>,<font color="Maroon" title="c1">n</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">i</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>   st <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c2">i</font></span>)</span> holds <br/>for <font color="Olive" title="b2">s</font> being  <a href="scmnorm.html#NM1" title="SCMNORM:NM.1">preProgram</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds   <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Olive" title="b2">s</font></span>)</span>,<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Olive" title="b2">s</font>,<font color="Maroon" title="c1">n</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c2">i</font></span>)</span> implies for <font color="Olive" title="b1">s</font> being  <a href="scmnorm.html#NM1" title="SCMNORM:NM.1">preProgram</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds   <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c1">n</font></span>)</span> )</span><br/>





<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E20">A1</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c2">i</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="scmnorm.html#NM1" title="SCMNORM:NM.1">preProgram</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds   <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c1">n</font></span>)</span></span><br/>

<a NAME="E2:21"/><i><font color="Green" title="E21">A2</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_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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="E3:21"/><i><font color="Green" title="E22">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_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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="E4:21"/><i><font color="Green" title="E23">A4</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_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">n</font></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#T14" title="FUNCOP_1:th.14">FUNCOP_1:14</a></i>;<br/>
<a NAME="E5:21"/><i><font color="Green" title="E24">A5</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></i>;<br/>
<i><font color="Green" title="E25">A6</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="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E2:21"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>
<br/>.= 
the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
<b>by </b><i><a class="txt" href="scmfsa_4.html#E5:21"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="zfmisc_1.html#T46" title="ZFMISC_1:th.46">ZFMISC_1:46</a></i>
;<br/>
<a NAME="E7:21"/><i><font color="Green" title="E26">A7</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></i>;<br/>
<a NAME="E8:21"/><i><font color="Green" title="E27">A8</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="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">n</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="scmfsa_4.html#E4:21"><i><font color="Green" title="E23">A4</font></i></a>, <a class="ref" href="funct_4.html#T18" title="FUNCT_4:th.18">FUNCT_4:18</a></i>;<br/>
<a NAME="E9:21"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">n</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 
<b>by </b><i><a class="txt" href="scmfsa_4.html#E7:21"><i><font color="Green" title="E26">A7</font></i></a>, <a class="ref" href="zfmisc_1.html#T46" title="ZFMISC_1:th.46">ZFMISC_1:46</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">g</font> = <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <b>by </b><i><a class="txt" href="scmfsa_4.html#E6:21"><i><font color="Green" title="E25">A6</font></i></a>, <a class="txt" href="scmfsa_4.html#E8:21"><i><font color="Green" title="E27">A8</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>;<br/>
<b>let </b><font color="Maroon" title="c5">s</font> be   <a href="scmnorm.html#NM1" title="SCMNORM:NM.1">preProgram</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c1">n</font></span>)</span></span><br/>

<a NAME="E11:21"/><i><font color="Green" title="E28">A9</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c1">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T119" title="AMI_1:th.119">AMI_1:119</a></i>;<br/>
<i><font color="Green" title="E29">A10</font></i>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c1">n</font></span>)</span> = 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">s</font>
<b>by </b><i><a class="ref" href="scmfsa_4.html#D6" target="_self" title="SCMFSA_4:def.6">Def6</a></i>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Maroon" title="c5">s</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T119" title="AMI_1:th.119">AMI_1:119</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">m</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</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"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Maroon" title="c5">s</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span>,<font color="Maroon" title="c1">n</font> )</span><br/><b>assume </b><a NAME="E1:21_3"/><i><font color="Green" title="E30">A11</font></i>: 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</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"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Maroon" title="c5">s</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span>,<font color="Maroon" title="c1">n</font></span><br/><a NAME="E2:21_3"/><b>then </b><i><font color="Green" title="E31">A12</font></i>: 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</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> <font color="Maroon" title="c5">s</font>
 <b>by </b><i><a class="ref" href="ami_1.html#T119" title="AMI_1:th.119">AMI_1:119</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_3_1"/>
( <font color="Maroon" title="c5">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  or <font color="Maroon" title="c5">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_3_1_1"><b>suppose </b></a><a NAME="E1:21_3_1_1"/><i><font color="Green" title="E32">A13</font></i>: 
<font color="Maroon" title="c5">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span>,<font color="Maroon" title="c1">n</font></span><br/><div class="add"><i><font color="Green" title="E33">A14</font></i>: <span class="p1">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</font></span>)</span> = 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c6">m</font></span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E2:21_3"><i><font color="Green" title="E31">A12</font></i></a>, <a class="ref" href="scmfsa_4.html#T24" target="_self" title="SCMFSA_4:th.24">Th24</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E2:21_3"><i><font color="Green" title="E31">A12</font></i></a>, <a class="txt" href="scmfsa_4.html#E1:21_3_1_1"><i><font color="Green" title="E32">A13</font></i></a>, <a class="ref" href="ami_1.html#D47" title="AMI_1:def.47">AMI_1:def 47</a></i>
<br/>.= 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
<b>by </b><i><a class="ref" href="scmfsa_4.html#T8" target="_self" title="SCMFSA_4:th.8">Th8</a></i>
;<br/><a NAME="E3:21_3_1_1"/><i><font color="Green" title="E34">A15</font></i>: 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <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#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></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/><i><font color="Green" title="E35">A16</font></i>:  <a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c6">m</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E1:21_3"><i><font color="Green" title="E30">A11</font></i></a>, <a class="ref" href="ami_1.html#D47" title="AMI_1:def.47">AMI_1:def 47</a></i>
<br/>.= 
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E2:21_3"><i><font color="Green" title="E31">A12</font></i></a>, <a class="txt" href="scmfsa_4.html#E1:21_3_1_1"><i><font color="Green" title="E32">A13</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E1:21"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="scmfsa_4.html#E3:21"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="scmfsa_4.html#E3:21_3_1_1"><i><font color="Green" title="E34">A15</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon" title="c2">i</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</font></span>)</span> = 
<font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E12:21"><i><font color="Green" title="E29">A10</font></i></a>, <a class="txt" href="scmfsa_4.html#E1:21_3"><i><font color="Green" title="E30">A11</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E2:21"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="scmfsa_4.html#E2:21_3_1_1"><i><font color="Green" title="E33">A14</font></i></a>, <a class="txt" href="scmfsa_4.html#E3:21_3_1_1"><i><font color="Green" title="E34">A15</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c6">m</font></span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E2:21_3_1_1"><i><font color="Green" title="E33">A14</font></i></a>, <a class="txt" href="scmfsa_4.html#E4:21_3_1_1"><i><font color="Green" title="E35">A16</font></i></a>, <a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</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="21_3_1_2"><b>suppose </b></a><a NAME="E1:21_3_1_2"/><i><font color="Green" title="E32">A17</font></i>: 
<font color="Maroon" title="c5">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span>,<font color="Maroon" title="c1">n</font></span><br/><div class="add"><a NAME="E2:21_3_1_2"/><i><font color="Green" title="E33">A18</font></i>: 
 <a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c6">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_4.html#E2:21_3"><i><font color="Green" title="E31">A12</font></i></a>, <a class="ref" href="ami_1.html#D47" title="AMI_1:def.47">AMI_1:def 47</a></i>;<br/><a NAME="E3:21_3_1_2"/><b>then </b><i><font color="Green" title="E34">A19</font></i>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c6">m</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="scmfsa_4.html#E1:21_3_1_2"><i><font color="Green" title="E32">A17</font></i></a>, <a class="ref" href="scmfsa_2.html#T122" title="SCMFSA_2:th.122">SCMFSA_2:122</a></i>;<br/><a NAME="E4:21_3_1_2"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c6">m</font></span>)</span>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c6">m</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_4.html#T22" target="_self" title="SCMFSA_4:th.22">Th22</a></i>;<br/><a NAME="E5:21_3_1_2"/><b>then </b><i><font color="Green" title="E35">A20</font></i>: 
not  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c6">m</font></span>)</span>,<font color="Maroon" title="c1">n</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#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa_4.html#E3:21_3_1_2"><i><font color="Green" title="E34">A19</font></i></a>, <a class="ref" href="scmfsa_2.html#T124" title="SCMFSA_2:th.124">SCMFSA_2:124</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E6:21_3_1_2"/><i><font color="Green" title="E36">A21</font></i>: 
not  <a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c6">m</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#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa_4.html#E1:21_3_1_2"><i><font color="Green" title="E32">A17</font></i></a>, <a class="txt" href="scmfsa_4.html#E2:21_3_1_2"><i><font color="Green" title="E33">A18</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><i><font color="Green" title="E37">A22</font></i>:  <a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c6">m</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E1:21_3"><i><font color="Green" title="E30">A11</font></i></a>, <a class="ref" href="ami_1.html#D47" title="AMI_1:def.47">AMI_1:def 47</a></i>
<br/>.= 
<font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E2:21_3"><i><font color="Green" title="E31">A12</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c6">m</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E1:21"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="scmfsa_4.html#E3:21"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="scmfsa_4.html#E2:21_3_1_2"><i><font color="Green" title="E33">A18</font></i></a>, <a class="txt" href="scmfsa_4.html#E6:21_3_1_2"><i><font color="Green" title="E36">A21</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
 <a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c6">m</font>
<b>by </b><i><a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</font></span>)</span> = 
<font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c6">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E12:21"><i><font color="Green" title="E29">A10</font></i></a>, <a class="txt" href="scmfsa_4.html#E1:21_3"><i><font color="Green" title="E30">A11</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c6">m</font></span>)</span>,<font color="Maroon" title="c1">n</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E2:21_3"><i><font color="Green" title="E31">A12</font></i></a>, <a class="ref" href="scmfsa_4.html#D6" target="_self" title="SCMFSA_4:def.6">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c6">m</font></span>)</span>,<font color="Maroon" title="c1">n</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E2:21"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="scmfsa_4.html#E5:21_3_1_2"><i><font color="Green" title="E35">A20</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">pi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c6">m</font></span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E7:21_3_1_2"><i><font color="Green" title="E37">A22</font></i></a>, <a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</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="E14:21"/>
 <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="ami_1.html#K38" title="AMI_1:func.38">*</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c1">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_4.html#E11:21"><i><font color="Green" title="E28">A9</font></i></a>, <a class="txt" href="scmfsa_4.html#E12:21"><i><font color="Green" title="E29">A10</font></i></a>, <a class="ref" href="scmfsa_4.html#D6" target="_self" title="SCMFSA_4:def.6">Def6</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>
