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

<span class="kw">let </span><font color="Maroon" title="c2">P</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a><br/>  for <font color="Olive" title="b2">i</font> being   <a href="scmpds_5.html#V1" title="SCMPDS_5:attr.1">parahalting</a>  <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> holds   <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Olive" title="b2">i</font>,<font color="Olive" title="b1">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <font color="Olive" title="b2">i</font></span>)</span>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b1">s</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">s</font> be   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">i</font> being   <a href="scmpds_5.html#V1" title="SCMPDS_5:attr.1">parahalting</a>  <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> holds   <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c3">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <font color="Olive" title="b1">i</font></span>)</span>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">s</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">i</font> be   <a href="scmpds_5.html#V1" title="SCMPDS_5:attr.1">parahalting</a>  <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <font color="Maroon" title="c4">i</font></span>)</span>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">s</font>)</span><br/>





<span class="kw">set </span><font color="Maroon" title="c5">Li</font> =  <a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <font color="Maroon" title="c4">i</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">Mi</font> =  <a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">PI</font> = <font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">IC1</font> =  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,1)</span>)</span>;<br/>
<a NAME="E1:65"/><span class="lab"><font color="Green" title="E29">I</font></span>: 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T44" title="MEMSTR_0:th.44">MEMSTR_0:44</a></span>;<br/>
<a NAME="E2:65"/>
 <a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/>
<a NAME="E3:65"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A2</font></span>: 
<font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c3">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#D7" title="SCMPDS_4:def.7">SCMPDS_4:def 7</a></span>;<br/>
<a NAME="E4:65"/><span class="lab"><font color="Green" title="E31">A3</font></span>: 
1 <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="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T57" title="COMPOS_1:th.57">COMPOS_1:57</a></span>;<br/>
<a NAME="E5:65"/><span class="lab"><font color="Green" title="E32">A4</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T57" title="COMPOS_1:th.57">COMPOS_1:57</a></span>;<br/>
<a NAME="E6:65"/><span class="lab"><font color="Green" title="E33">A22</font></span>: 
<span class="p1">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T59" title="COMPOS_1:th.59">COMPOS_1:59</a></span>;<br/>
<a NAME="E7:65"/><span class="lab"><font color="Green" title="E34">A23</font></span>: 
<span class="p1">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T58" title="COMPOS_1:th.58">COMPOS_1:58</a></span>;<br/>
<a NAME="E8:65"/><span class="lab"><font color="Green" title="E35">A24</font></span>: 
 <a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/>
<a NAME="E9:65"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A25</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,1)</span>)</span> <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="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#D6" title="SCMPDS_4:def.6">SCMPDS_4:def 6</a></span>;<br/>
<a NAME="E10:65"/><span class="lab"><font color="Green" title="E37">A26</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c3">s</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T143" title="PBOOLE:th.143">PBOOLE:143</a></span>;<br/>
<span class="lab"><font color="Green" title="E38">A27</font></span>:  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<font color="Maroon" title="c3">s</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:65"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="ref" href="memstr_0.html#T47" title="MEMSTR_0:th.47">MEMSTR_0:47</a>, <a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E29">I</font></span></a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:65"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E7:65"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="txt" href="#E8:65"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_2"><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="E1:65_2"/>
(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:65"><span class="lab"><font color="Green" title="E36">A25</font></span></a>, <a class="ref" href="compos_1.html#T60" title="COMPOS_1:th.60">COMPOS_1:60</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_2_1"><span class="kw">suppose </span></a><a NAME="E1:65_2_1"/><span class="lab"><font color="Green" title="E39">A28</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <font color="Maroon" title="c4">i</font></span>)</span>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">s</font>)</span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c9">Ni</font> =  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font>;<br/> <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> = 
 <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T47" title="MEMSTR_0:th.47">MEMSTR_0:47</a>, <a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E29">I</font></span></a></span>
<br/>.= 
1

;<br/><a NAME="E3:65_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A29</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1,4,5,6</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:65"><span class="lab"><font color="Green" title="E38">A27</font></span></a>, <a class="txt" href="#E1:65_2_1"><span class="lab"><font color="Green" title="E39">A28</font></span></a>, <a class="ref" href="scmpds_4.html#T1" title="SCMPDS_4:th.1">SCMPDS_4:1</a></span>;<br/><span class="lab"><font color="Green" title="E41">A30</font></span>:  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,1)</span>)</span>) = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65_2_1"><span class="lab"><font color="Green" title="E39">A28</font></span></a>, <a class="ref" href="pboole.html#T143" title="PBOOLE:th.143">PBOOLE:143</a></span>
<br/>.= 
<font color="Maroon" title="c4">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:65"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E7:65"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="txt" href="#E8:65"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
;<br/><a NAME="E5:65_2_1"/><span class="lab"><font color="Green" title="E42">A31</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T22" target="_self" title="SCMPDS_5:th.22">Th26</a></span>;<br/><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_2_1_3_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="E1:65_2_1_3_1"/>
( <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> or <font color="Maroon" title="c4">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_2_1_3_1_1"><span class="kw">suppose </span></a><a NAME="E1:65_2_1_3_1_1"/>
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <font color="Maroon" title="c4">i</font></span>)</span>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">s</font>)</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:65_2_1_3_1_1"/>
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <font color="Maroon" title="c4">i</font></span>)</span>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">s</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E11:65"><span class="lab"><font color="Green" title="E38">A27</font></span></a>, <a class="txt" href="#E4:65_2_1"><span class="lab"><font color="Green" title="E41">A30</font></span></a>, <a class="ref" href="extpro_1.html#D9" title="EXTPRO_1:def.9">EXTPRO_1:def 9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="65_2_1_3_1_2"><span class="kw">suppose </span></a><a NAME="E1:65_2_1_3_1_2"/><span class="lab"><font color="Green" title="E43">A32</font></span>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <font color="Maroon" title="c4">i</font></span>)</span>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">s</font>)</span><br/><div class="add"><div><span class="lab"><font color="Green" title="E44">A34</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="65_2_1_3_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c10">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_2_1_3_1_2_1_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="E1:65_2_1_3_1_2_1_1"/>
(  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65_2_1"><span class="lab"><font color="Green" title="E40">A29</font></span></a>, <a class="txt" href="#E5:65_2_1"><span class="lab"><font color="Green" title="E42">A31</font></span></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_2_1_3_1_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:65_2_1_3_1_2_1_1_1"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:65_2_1_3_1_2_1_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">k1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <font color="Olive" title="b1">k1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T26" title="SCMPDS_2:th.26">SCMPDS_2:26</a></span>;<br/><span class="kw">hence </span><a NAME="E3:65_2_1_3_1_2_1_1_1"/>
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T54" title="SCMPDS_2:th.54">SCMPDS_2:54</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="65_2_1_3_1_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:65_2_1_3_1_2_1_1_2"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:65_2_1_3_1_2_1_1_2"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font>, <font color="Olive" title="b3">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">k1</font>) <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <font color="Olive" title="b3">k2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T30" title="SCMPDS_2:th.30">SCMPDS_2:30</a></span>;<br/><span class="kw">hence </span><a NAME="E3:65_2_1_3_1_2_1_1_2"/>
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T55" title="SCMPDS_2:th.55">SCMPDS_2:55</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="65_2_1_3_1_2_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:65_2_1_3_1_2_1_1_3"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:65_2_1_3_1_2_1_1_3"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font>, <font color="Olive" title="b3">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">k1</font>) <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Olive" title="b3">k2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T31" title="SCMPDS_2:th.31">SCMPDS_2:31</a></span>;<br/><span class="kw">hence </span><a NAME="E3:65_2_1_3_1_2_1_1_3"/>
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T56" title="SCMPDS_2:th.56">SCMPDS_2:56</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="65_2_1_3_1_2_1_1_4"><span class="kw">suppose </span></a><a NAME="E1:65_2_1_3_1_2_1_1_4"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:65_2_1_3_1_2_1_1_4"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font>, <font color="Olive" title="b3">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">k1</font>) <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <font color="Olive" title="b3">k2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T32" title="SCMPDS_2:th.32">SCMPDS_2:32</a></span>;<br/><span class="kw">hence </span><a NAME="E3:65_2_1_3_1_2_1_1_4"/>
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c10">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="lab"><font color="Green" title="E45">A35</font></span>:  <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:65"><span class="lab"><font color="Green" title="E38">A27</font></span></a>, <a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</a></span>
;<br/><a NAME="E4:65_2_1_3_1_2"/><span class="lab"><font color="Green" title="E46">A36</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:65"><span class="lab"><font color="Green" title="E38">A27</font></span></a>, <a class="txt" href="#E1:65_2_1"><span class="lab"><font color="Green" title="E39">A28</font></span></a>, <a class="ref" href="memstr_0.html#T47" title="MEMSTR_0:th.47">MEMSTR_0:47</a>, <a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E29">I</font></span></a></span>;<br/><a NAME="E5:65_2_1_3_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A37</font></span>: 
<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65_2_1_3_1_2"><span class="lab"><font color="Green" title="E44">A34</font></span></a>, <a class="ref" href="scmpds_2.html#T44" title="SCMPDS_2:th.44">SCMPDS_2:44</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_2_1_3_1_2_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c10">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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c10">n</font>)</span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a></span><br/> <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c10">n</font>) = 
<font color="Maroon" title="c3">s</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:65_2_1_3_1_2"><span class="lab"><font color="Green" title="E46">A36</font></span></a>, <a class="txt" href="#E2:65_2_1_3_1_2"><span class="lab"><font color="Green" title="E44">A34</font></span></a>, <a class="txt" href="#E3:65_2_1_3_1_2"><span class="lab"><font color="Green" title="E45">A35</font></span></a>, <a class="ref" href="extpro_1.html#T27" title="EXTPRO_1:th.27">EXTPRO_1:27</a>, <a class="ref" href="scmpds_2.html#T44" title="SCMPDS_2:th.44">SCMPDS_2:44</a></span>
<br/>.= 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:65_2_1_3_1_2"><span class="lab"><font color="Green" title="E47">A37</font></span></a>, <a class="txt" href="#E3:65_2_1_3_1_2"><span class="lab"><font color="Green" title="E45">A35</font></span></a>, <a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a></span>
<br/>.= 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</a></span>
;<br/><span class="kw">hence </span><a NAME="E2:65_2_1_3_1_2_3"/>
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c10">n</font>)</span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:65_2_1"><span class="lab"><font color="Green" title="E41">A30</font></span></a>, <a class="txt" href="#E1:65_2_1_3_1_2"><span class="lab"><font color="Green" title="E43">A32</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E7:65_2_1_3_1_2"/><span class="kw">then </span>
 not <font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c3">s</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T29" title="EXTPRO_1:th.29">EXTPRO_1:29</a></span>;<br/><span class="kw">hence </span><a NAME="E8:65_2_1_3_1_2"/>
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <font color="Maroon" title="c4">i</font></span>)</span>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">s</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:65"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="scmpds_4.html#D7" title="SCMPDS_4:def.7">SCMPDS_4:def 7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_2_2"><span class="kw">suppose </span></a><a NAME="E1:65_2_2"/><span class="lab"><font color="Green" title="E39">A38</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <font color="Maroon" title="c4">i</font></span>)</span>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">s</font>)</span><br/><div class="add"> <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,1)</span>)</span>) = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65_2_2"><span class="lab"><font color="Green" title="E39">A38</font></span></a>, <a class="ref" href="pboole.html#T143" title="PBOOLE:th.143">PBOOLE:143</a></span>
<br/>.= 
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:65"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="txt" href="#E6:65"><span class="lab"><font color="Green" title="E33">A22</font></span></a>, <a class="txt" href="#E8:65"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:65_2_2"/>
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <font color="Maroon" title="c4">i</font></span>)</span>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">s</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E11:65"><span class="lab"><font color="Green" title="E38">A27</font></span></a>, <a class="ref" href="extpro_1.html#D9" title="EXTPRO_1:def.9">EXTPRO_1:def 9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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>
