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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">S</font> being   <a href="compos_1.html#V3" title="COMPOS_1:attr.3">standard-ins</a>   <a href="compos_1.html#V6" title="COMPOS_1:attr.6">homogeneous</a>   <a href="compos_1.html#V7" title="COMPOS_1:attr.7">regular</a>   <a href="compos_1.html#V8" title="COMPOS_1:attr.8">J/A-independent</a>   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="memstr_0.html#V2" title="MEMSTR_0:attr.2">IC-Ins-separated</a>   <a href="extpro_1.html#V3" title="EXTPRO_1:attr.3">halting</a>   <a href="amistd_2.html#V2" title="AMISTD_2:attr.2">with_explicit_jumps</a>   <a href="extpro_1.html#L1" title="EXTPRO_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font><br/>  for <font color="Olive" title="b2">I</font> being   <a href="amistd_2.html#V3" title="AMISTD_2:attr.3">IC-relocable</a>  <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <font color="Olive" title="b1">S</font><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> <br/>  for <font color="Olive" title="b4">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <font color="Olive" title="b1">S</font> holds  <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Olive" title="b2">I</font>,<font color="Olive" title="b4">s</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b3">k</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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Olive" title="b2">I</font>,<font color="Olive" title="b3">k</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive" title="b4">s</font>,<font color="Olive" title="b3">k</font>)</span>)</span>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="compos_1.html#V3" title="COMPOS_1:attr.3">standard-ins</a>   <a href="compos_1.html#V6" title="COMPOS_1:attr.6">homogeneous</a>   <a href="compos_1.html#V7" title="COMPOS_1:attr.7">regular</a>   <a href="compos_1.html#V8" title="COMPOS_1:attr.8">J/A-independent</a>   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="memstr_0.html#V2" title="MEMSTR_0:attr.2">IC-Ins-separated</a>   <a href="extpro_1.html#V3" title="EXTPRO_1:attr.3">halting</a>   <a href="amistd_2.html#V2" title="AMISTD_2:attr.2">with_explicit_jumps</a>   <a href="extpro_1.html#L1" title="EXTPRO_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>; <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="amistd_2.html#V3" title="AMISTD_2:attr.3">IC-relocable</a>  <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <font color="Maroon" title="c2">S</font><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> <br/>  for <font color="Olive" title="b3">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <font color="Maroon" title="c2">S</font> holds  <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<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="b3">s</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b2">k</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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">k</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive" title="b3">s</font>,<font color="Olive" title="b2">k</font>)</span>)</span>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">I</font> be   <a href="amistd_2.html#V3" title="AMISTD_2:attr.3">IC-relocable</a>  <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <font color="Maroon" title="c2">S</font>; <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> <br/>  for <font color="Olive" title="b2">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <font color="Maroon" title="c2">S</font> holds  <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c3">I</font>,<font color="Olive" title="b2">s</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b1">k</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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c3">I</font>,<font color="Olive" title="b1">k</font>)</span>)</span>,<span class="p2">(<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="b1">k</font>)</span>)</span>)</span>)</span></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">  for <font color="Olive" title="b1">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <font color="Maroon" title="c2">S</font> holds  <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c3">I</font>,<font color="Olive" title="b1">s</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c4">k</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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">k</font>)</span>)</span>,<span class="p2">(<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="Maroon" title="c4">k</font>)</span>)</span>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">s</font> be   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c5">s</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c4">k</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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">k</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">k</font>)</span>)</span>)</span>)</span></span><br/>









<a NAME="E1:35"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
<font color="Maroon" title="c4">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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">k</font>
 
;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c5">s</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c4">k</font> = 
<span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c3">I</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span>,<font color="Maroon" title="c5">s</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c4">k</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T10" title="COMPOS_1:th.10">COMPOS_1:10</a></span>
<br/>.= 
 <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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">k</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">k</font>)</span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_2.html#D3" target="_self" title="AMISTD_2:def.3">Def18</a>, <a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E12">A1</font></span></a></span>
<br/>.= 
 <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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">k</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">k</font>)</span>)</span>)</span>)</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/>


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