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<span class="kw">let </span><font color="Maroon" title="c1">N</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span><br/>  for <font color="Olive" title="b2">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span><br/>  for <font color="Olive" title="b3">k</font> being   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  holds   <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Olive" title="b1">I</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive" title="b2">s</font>,<font color="Olive" title="b3">k</font>)</span>)</span>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">s</font>)</span>)</span>,<font color="Olive" title="b3">k</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">I</font> be   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span>; <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="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span><br/>  for <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  holds   <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">I</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">k</font>)</span>)</span>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">I</font>,<font color="Olive" title="b1">s</font>)</span>)</span>,<font color="Olive" title="b2">k</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">s</font> be   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span>; <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">k</font> being   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  holds   <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">I</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c3">s</font>,<font color="Olive" title="b1">k</font>)</span>)</span>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s</font>)</span>)</span>,<font color="Olive" title="b1">k</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">k</font> be   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</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="c2">I</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">k</font>)</span>)</span>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)</span><br/>







<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="6_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="E1:6_1"/>
(  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_1.html#T6" title="AMISTD_1:th.6">AMISTD_1:6</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="6_1_1"><span class="kw">suppose </span></a><a NAME="E1:6_1_1"/><span class="lab"><font color="Green" title="E4">A1</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">I</font> <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="c2">I</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">k</font>)</span>)</span>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)</span><br/><div class="add"><span class="kw">hence </span> <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">I</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">k</font>)</span>)</span>) = 
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">k</font>)</span>)</span>,1)
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_1.html#T20" title="AMISTD_1:th.20">AMISTD_1:20</a></span>
<br/>.= 
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T57" title="MEMSTR_0:th.57">MEMSTR_0:57</a></span>
<br/>.= 
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c3">s</font>,1)</span>)</span>,<font color="Maroon" title="c4">k</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T57" title="MEMSTR_0:th.57">MEMSTR_0:57</a></span>
<br/>.= 
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_1_1"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="amistd_1.html#T20" title="AMISTD_1:th.20">AMISTD_1:20</a></span>
;<br/> <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="6_1_2"><span class="kw">suppose </span></a><a NAME="E1:6_1_2"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">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">  <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">I</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">k</font>)</span>)</span>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)</span><br/><div class="add"><a NAME="E2:6_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E4">A2</font></span>: 
<font color="Maroon" title="c2">I</font> is  <a href="extpro_1.html#V2" title="EXTPRO_1:attr.2">halting</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_1.html#T4" title="AMISTD_1:th.4">AMISTD_1:4</a></span>;<br/><span class="kw">hence </span> <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">I</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">k</font>)</span>)</span>) = 
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">k</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#D3" title="EXTPRO_1:def.3">EXTPRO_1:def 3</a></span>
<br/>.= 
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1_2"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="extpro_1.html#D3" title="EXTPRO_1:def.3">EXTPRO_1:def 3</a></span>
;<br/> <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>

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