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<span class="kw">let </span><font color="Maroon" title="c2">INS</font> be   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="amistd_5.html#D2" title="AMISTD_5:def.2">AMISTD_5:def 2</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="c2">INS</font> is  <a href="amistd_5.html#V1" title="AMISTD_5:attr.1">relocable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">j</font>, <font color="Maroon" title="c4">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="amistd_5.html#D1" title="AMISTD_5:def.1">AMISTD_5:def 1</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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds   <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive">b<sub>1</sub></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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Olive">b<sub>1</sub></font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)</span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c5">k</font> = <font color="Maroon" title="c4">k</font> as    <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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c6">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="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>; <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> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)</span><br/>

<span class="lab"><font color="Green" title="E4">A1</font></span>:  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</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> (<span class="p3">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c5">k</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T53" title="MEMSTR_0:th.53">MEMSTR_0:53</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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_2.html#D3" title="AMISTD_2:def.3">AMISTD_2:def 3</a></span>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_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="E1:7_1_1_2"/>
(  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">INS</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="c2">INS</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">INS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">INS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">INS</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="c2">INS</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="c2">INS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">INS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T31" title="NAT_1:th.31">NAT_1:31</a>, <a class="ref" href="scmring3.html#T39" title="SCMRING3:th.39">SCMRING3:39</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_1"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_1"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">INS</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> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)</span><br/><div class="add"><a NAME="E2:7_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A3</font></span>: 
<font color="Maroon" title="c2">INS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T12" title="SCMRING3:th.12">SCMRING3:12</a></span>;<br/> <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>) = 
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7_1_1_2_1"><span class="lab"><font color="Green" title="E5">A3</font></span></a>, <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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7_1_1_2_1"><span class="lab"><font color="Green" title="E5">A3</font></span></a>, <a class="ref" href="extpro_1.html#D3" title="EXTPRO_1:def.3">EXTPRO_1:def 3</a></span>
;<br/><span class="kw">hence </span><a NAME="E4:7_1_1_2_1"/>
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)
 ; <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="7_1_1_2_2"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_2"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">INS</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> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">da</font>, <font color="Maroon" title="c8">db</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font><span class="kw"> such that </span><br/><a NAME="E3:7_1_1_2_2"/><span class="lab"><font color="Green" title="E5">A4</font></span>: 
<font color="Maroon" title="c2">INS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">:=</a> <font color="Maroon" title="c8">db</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T13" title="SCMRING3:th.13">SCMRING3:13</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_1_2_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">d</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2: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="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_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="E1:7_1_1_2_2_1_1"/>
( <font color="Maroon" title="c7">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">d</font> or <font color="Maroon" title="c7">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_2_1_1_1"/><span class="lab"><font color="Green" title="E6">A5</font></span>: 
<font color="Maroon" title="c7">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">d</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2: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="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">thus </span><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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_2"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">db</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_2"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="txt" href="#E1:7_1_1_2_2_1_1_1"><span class="lab"><font color="Green" title="E6">A5</font></span></a>, <a class="ref" href="scmring2.html#T11" title="SCMRING2:th.11">SCMRING2:11</a></span>
<br/>.= 
<font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">db</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_2"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="txt" href="#E1:7_1_1_2_2_1_1_1"><span class="lab"><font color="Green" title="E6">A5</font></span></a>, <a class="ref" href="scmring2.html#T11" title="SCMRING2:th.11">SCMRING2:11</a></span>
<br/>.= 
<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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_2"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</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="7_1_1_2_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_2_1_1_2"/><span class="lab"><font color="Green" title="E6">A6</font></span>: 
<font color="Maroon" title="c7">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">d</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2: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="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">thus </span><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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_2"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_2"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="txt" href="#E1:7_1_1_2_2_1_1_2"><span class="lab"><font color="Green" title="E6">A6</font></span></a>, <a class="ref" href="scmring2.html#T11" title="SCMRING2:th.11">SCMRING2:11</a></span>
<br/>.= 
<font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_2"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="txt" href="#E1:7_1_1_2_2_1_1_2"><span class="lab"><font color="Green" title="E6">A6</font></span></a>, <a class="ref" href="scmring2.html#T11" title="SCMRING2:th.11">SCMRING2:11</a></span>
<br/>.= 
<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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_2"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</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="kw">hence </span><a NAME="E5:7_1_1_2_2"/>
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T6" target="_self" title="SCMRING4:th.6">Th8</a>, <a class="txt" href="#E2:7_1_1"><span class="lab"><font color="Green" title="E4">A1</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_3"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_3"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">INS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <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> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">da</font>, <font color="Maroon" title="c8">db</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font><span class="kw"> such that </span><br/><a NAME="E3:7_1_1_2_3"/><span class="lab"><font color="Green" title="E5">A7</font></span>: 
<font color="Maroon" title="c2">INS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K4" title="SCMRING2:func.4">AddTo</a> (<font color="Maroon" title="c7">da</font>,<font color="Maroon" title="c8">db</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T14" title="SCMRING3:th.14">SCMRING3:14</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_1_2_3_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">d</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2: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="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_3_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="E1:7_1_1_2_3_1_1"/>
( <font color="Maroon" title="c7">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">d</font> or <font color="Maroon" title="c7">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_3_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_3_1_1_1"/><span class="lab"><font color="Green" title="E6">A8</font></span>: 
<font color="Maroon" title="c7">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">d</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2: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="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">thus </span><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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_3"><span class="lab"><font color="Green" title="E5">A7</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c7">da</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7_1_1_2_3_1_1_1"><span class="lab"><font color="Green" title="E6">A8</font></span></a>, <a class="txt" href="#E3:7_1_1_2_3"><span class="lab"><font color="Green" title="E5">A7</font></span></a>, <a class="ref" href="scmring2.html#T12" title="SCMRING2:th.12">SCMRING2:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c7">da</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c7">da</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_3"><span class="lab"><font color="Green" title="E5">A7</font></span></a>, <a class="txt" href="#E1:7_1_1_2_3_1_1_1"><span class="lab"><font color="Green" title="E6">A8</font></span></a>, <a class="ref" href="scmring2.html#T12" title="SCMRING2:th.12">SCMRING2:12</a></span>
<br/>.= 
<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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_3"><span class="lab"><font color="Green" title="E5">A7</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</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="7_1_1_2_3_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_3_1_1_2"/><span class="lab"><font color="Green" title="E6">A9</font></span>: 
<font color="Maroon" title="c7">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">d</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2: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="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">thus </span><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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_3"><span class="lab"><font color="Green" title="E5">A7</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_3"><span class="lab"><font color="Green" title="E5">A7</font></span></a>, <a class="txt" href="#E1:7_1_1_2_3_1_1_2"><span class="lab"><font color="Green" title="E6">A9</font></span></a>, <a class="ref" href="scmring2.html#T12" title="SCMRING2:th.12">SCMRING2:12</a></span>
<br/>.= 
<font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_3"><span class="lab"><font color="Green" title="E5">A7</font></span></a>, <a class="txt" href="#E1:7_1_1_2_3_1_1_2"><span class="lab"><font color="Green" title="E6">A9</font></span></a>, <a class="ref" href="scmring2.html#T12" title="SCMRING2:th.12">SCMRING2:12</a></span>
<br/>.= 
<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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_3"><span class="lab"><font color="Green" title="E5">A7</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</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="kw">hence </span><a NAME="E5:7_1_1_2_3"/>
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T6" target="_self" title="SCMRING4:th.6">Th8</a>, <a class="txt" href="#E2:7_1_1"><span class="lab"><font color="Green" title="E4">A1</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_4"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_4"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">INS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ; <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> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">da</font>, <font color="Maroon" title="c8">db</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font><span class="kw"> such that </span><br/><a NAME="E3:7_1_1_2_4"/><span class="lab"><font color="Green" title="E5">A10</font></span>: 
<font color="Maroon" title="c2">INS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K5" title="SCMRING2:func.5">SubFrom</a> (<font color="Maroon" title="c7">da</font>,<font color="Maroon" title="c8">db</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T15" title="SCMRING3:th.15">SCMRING3:15</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_1_2_4_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">d</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2: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="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_4_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="E1:7_1_1_2_4_1_1"/>
( <font color="Maroon" title="c7">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">d</font> or <font color="Maroon" title="c7">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_4_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_4_1_1_1"/><span class="lab"><font color="Green" title="E6">A11</font></span>: 
<font color="Maroon" title="c7">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">d</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2: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="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">thus </span><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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_4"><span class="lab"><font color="Green" title="E5">A10</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c7">da</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7_1_1_2_4_1_1_1"><span class="lab"><font color="Green" title="E6">A11</font></span></a>, <a class="txt" href="#E3:7_1_1_2_4"><span class="lab"><font color="Green" title="E5">A10</font></span></a>, <a class="ref" href="scmring2.html#T13" title="SCMRING2:th.13">SCMRING2:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c7">da</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c7">da</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_4"><span class="lab"><font color="Green" title="E5">A10</font></span></a>, <a class="txt" href="#E1:7_1_1_2_4_1_1_1"><span class="lab"><font color="Green" title="E6">A11</font></span></a>, <a class="ref" href="scmring2.html#T13" title="SCMRING2:th.13">SCMRING2:13</a></span>
<br/>.= 
<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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_4"><span class="lab"><font color="Green" title="E5">A10</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</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="7_1_1_2_4_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_4_1_1_2"/><span class="lab"><font color="Green" title="E6">A12</font></span>: 
<font color="Maroon" title="c7">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">d</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2: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="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">thus </span><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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_4"><span class="lab"><font color="Green" title="E5">A10</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_4"><span class="lab"><font color="Green" title="E5">A10</font></span></a>, <a class="txt" href="#E1:7_1_1_2_4_1_1_2"><span class="lab"><font color="Green" title="E6">A12</font></span></a>, <a class="ref" href="scmring2.html#T13" title="SCMRING2:th.13">SCMRING2:13</a></span>
<br/>.= 
<font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_4"><span class="lab"><font color="Green" title="E5">A10</font></span></a>, <a class="txt" href="#E1:7_1_1_2_4_1_1_2"><span class="lab"><font color="Green" title="E6">A12</font></span></a>, <a class="ref" href="scmring2.html#T13" title="SCMRING2:th.13">SCMRING2:13</a></span>
<br/>.= 
<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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_4"><span class="lab"><font color="Green" title="E5">A10</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</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="kw">hence </span><a NAME="E5:7_1_1_2_4"/>
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T6" target="_self" title="SCMRING4:th.6">Th8</a>, <a class="txt" href="#E2:7_1_1"><span class="lab"><font color="Green" title="E4">A1</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_5"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_5"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">INS</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">  <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">da</font>, <font color="Maroon" title="c8">db</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font><span class="kw"> such that </span><br/><a NAME="E3:7_1_1_2_5"/><span class="lab"><font color="Green" title="E5">A13</font></span>: 
<font color="Maroon" title="c2">INS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K6" title="SCMRING2:func.6">MultBy</a> (<font color="Maroon" title="c7">da</font>,<font color="Maroon" title="c8">db</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T16" title="SCMRING3:th.16">SCMRING3:16</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_1_2_5_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">d</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2: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="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_5_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="E1:7_1_1_2_5_1_1"/>
( <font color="Maroon" title="c7">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">d</font> or <font color="Maroon" title="c7">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_5_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_5_1_1_1"/><span class="lab"><font color="Green" title="E6">A14</font></span>: 
<font color="Maroon" title="c7">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">d</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2: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="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">thus </span><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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_5"><span class="lab"><font color="Green" title="E5">A13</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c7">da</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7_1_1_2_5_1_1_1"><span class="lab"><font color="Green" title="E6">A14</font></span></a>, <a class="txt" href="#E3:7_1_1_2_5"><span class="lab"><font color="Green" title="E5">A13</font></span></a>, <a class="ref" href="scmring2.html#T14" title="SCMRING2:th.14">SCMRING2:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c7">da</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c7">da</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_5"><span class="lab"><font color="Green" title="E5">A13</font></span></a>, <a class="txt" href="#E1:7_1_1_2_5_1_1_1"><span class="lab"><font color="Green" title="E6">A14</font></span></a>, <a class="ref" href="scmring2.html#T14" title="SCMRING2:th.14">SCMRING2:14</a></span>
<br/>.= 
<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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_5"><span class="lab"><font color="Green" title="E5">A13</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</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="7_1_1_2_5_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_5_1_1_2"/><span class="lab"><font color="Green" title="E6">A15</font></span>: 
<font color="Maroon" title="c7">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">d</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2: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="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">thus </span><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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_5"><span class="lab"><font color="Green" title="E5">A13</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_5"><span class="lab"><font color="Green" title="E5">A13</font></span></a>, <a class="txt" href="#E1:7_1_1_2_5_1_1_2"><span class="lab"><font color="Green" title="E6">A15</font></span></a>, <a class="ref" href="scmring2.html#T14" title="SCMRING2:th.14">SCMRING2:14</a></span>
<br/>.= 
<font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_5"><span class="lab"><font color="Green" title="E5">A13</font></span></a>, <a class="txt" href="#E1:7_1_1_2_5_1_1_2"><span class="lab"><font color="Green" title="E6">A15</font></span></a>, <a class="ref" href="scmring2.html#T14" title="SCMRING2:th.14">SCMRING2:14</a></span>
<br/>.= 
<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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_5"><span class="lab"><font color="Green" title="E5">A13</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</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="kw">hence </span><a NAME="E5:7_1_1_2_5"/>
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T6" target="_self" title="SCMRING4:th.6">Th8</a>, <a class="txt" href="#E2:7_1_1"><span class="lab"><font color="Green" title="E4">A1</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_6"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_6"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">INS</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">  <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">da</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>, <font color="Maroon" title="c8">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><span class="kw"> such that </span><br/><a NAME="E3:7_1_1_2_6"/><span class="lab"><font color="Green" title="E5">A16</font></span>: 
<font color="Maroon" title="c2">INS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</font> <a href="scmring2.html#K7" title="SCMRING2:func.7">:=</a> <font color="Maroon" title="c8">r</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T17" title="SCMRING3:th.17">SCMRING3:17</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_1_2_6_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">d</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2: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="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_6_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="E1:7_1_1_2_6_1_1"/>
( <font color="Maroon" title="c7">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">d</font> or <font color="Maroon" title="c7">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_6_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_6_1_1_1"/><span class="lab"><font color="Green" title="E6">A17</font></span>: 
<font color="Maroon" title="c7">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">d</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2: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="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">thus </span><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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_6"><span class="lab"><font color="Green" title="E5">A16</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<font color="Maroon" title="c8">r</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7_1_1_2_6_1_1_1"><span class="lab"><font color="Green" title="E6">A17</font></span></a>, <a class="txt" href="#E3:7_1_1_2_6"><span class="lab"><font color="Green" title="E5">A16</font></span></a>, <a class="ref" href="scmring2.html#T17" title="SCMRING2:th.17">SCMRING2:17</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_6"><span class="lab"><font color="Green" title="E5">A16</font></span></a>, <a class="txt" href="#E1:7_1_1_2_6_1_1_1"><span class="lab"><font color="Green" title="E6">A17</font></span></a>, <a class="ref" href="scmring2.html#T17" title="SCMRING2:th.17">SCMRING2:17</a></span>
<br/>.= 
<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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_6"><span class="lab"><font color="Green" title="E5">A16</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</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="7_1_1_2_6_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_6_1_1_2"/><span class="lab"><font color="Green" title="E6">A18</font></span>: 
<font color="Maroon" title="c7">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">d</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2: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="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">thus </span><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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_6"><span class="lab"><font color="Green" title="E5">A16</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_6"><span class="lab"><font color="Green" title="E5">A16</font></span></a>, <a class="txt" href="#E1:7_1_1_2_6_1_1_2"><span class="lab"><font color="Green" title="E6">A18</font></span></a>, <a class="ref" href="scmring2.html#T17" title="SCMRING2:th.17">SCMRING2:17</a></span>
<br/>.= 
<font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_6"><span class="lab"><font color="Green" title="E5">A16</font></span></a>, <a class="txt" href="#E1:7_1_1_2_6_1_1_2"><span class="lab"><font color="Green" title="E6">A18</font></span></a>, <a class="ref" href="scmring2.html#T17" title="SCMRING2:th.17">SCMRING2:17</a></span>
<br/>.= 
<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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_6"><span class="lab"><font color="Green" title="E5">A16</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</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="kw">hence </span><a NAME="E5:7_1_1_2_6"/>
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T6" target="_self" title="SCMRING4:th.6">Th8</a>, <a class="txt" href="#E2:7_1_1"><span class="lab"><font color="Green" title="E4">A1</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_7"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_7"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">INS</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">  <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">loc</font> being    <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> <span class="kw"> such that </span><br/><a NAME="E3:7_1_1_2_7"/><span class="lab"><font color="Green" title="E5">A19</font></span>: 
<font color="Maroon" title="c2">INS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K8" title="SCMRING2:func.8">goto</a> (<font color="Maroon" title="c7">loc</font>,<font color="Maroon" title="c1">R</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T18" title="SCMRING3:th.18">SCMRING3:18</a></span>;<br/><a NAME="E4:7_1_1_2_7"/><span class="lab"><font color="Green" title="E6">A20</font></span>: 
 <a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K8" title="SCMRING2:func.8">goto</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">R</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_7"><span class="lab"><font color="Green" title="E5">A19</font></span></a>, <a class="ref" href="scmring3.html#T37" title="SCMRING3:th.37">SCMRING3:37</a></span>;<br/><a NAME="E5:7_1_1_2_7"/><span class="lab"><font color="Green" title="E7">A21</font></span>: 
 <a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K8" title="SCMRING2:func.8">goto</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">j</font></span>)</span>,<font color="Maroon" title="c1">R</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_7"><span class="lab"><font color="Green" title="E5">A19</font></span></a>, <a class="ref" href="scmring3.html#T37" title="SCMRING3:th.37">SCMRING3:37</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_1_2_7_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">d</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">d</font></span><br/><span class="kw">thus </span><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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">d</font> = 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7_1_1_2_7"><span class="lab"><font color="Green" title="E6">A20</font></span></a>, <a class="ref" href="scmring2.html#T15" title="SCMRING2:th.15">SCMRING2:15</a></span>
<br/>.= 
<font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</a></span>
<br/>.= 
<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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7_1_1_2_7"><span class="lab"><font color="Green" title="E7">A21</font></span></a>, <a class="ref" href="scmring2.html#T15" title="SCMRING2:th.15">SCMRING2:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</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><span class="kw">hence </span><a NAME="E7:7_1_1_2_7"/>
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T6" target="_self" title="SCMRING4:th.6">Th8</a>, <a class="txt" href="#E2:7_1_1"><span class="lab"><font color="Green" title="E4">A1</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2_8"><span class="kw">suppose </span></a><a NAME="E1:7_1_1_2_8"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">INS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ; <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> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">da</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>, <font color="Maroon" title="c8">loc</font> being    <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> <span class="kw"> such that </span><br/><a NAME="E3:7_1_1_2_8"/><span class="lab"><font color="Green" title="E5">A22</font></span>: 
<font color="Maroon" title="c2">INS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</font> <a href="scmring2.html#K9" title="SCMRING2:func.9">=0_goto</a> <font color="Maroon" title="c8">loc</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T19" title="SCMRING3:th.19">SCMRING3:19</a></span>;<br/><a NAME="E4:7_1_1_2_8"/><span class="lab"><font color="Green" title="E6">A23</font></span>: 
 <a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</font> <a href="scmring2.html#K9" title="SCMRING2:func.9">=0_goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_8"><span class="lab"><font color="Green" title="E5">A22</font></span></a>, <a class="ref" href="scmring3.html#T38" title="SCMRING3:th.38">SCMRING3:38</a></span>;<br/><a NAME="E5:7_1_1_2_8"/><span class="lab"><font color="Green" title="E7">A24</font></span>: 
 <a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</font> <a href="scmring2.html#K9" title="SCMRING2:func.9">=0_goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7_1_1_2_8"><span class="lab"><font color="Green" title="E5">A22</font></span></a>, <a class="ref" href="scmring3.html#T38" title="SCMRING3:th.38">SCMRING3:38</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_1_2_8_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">d</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</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="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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font></span><br/><span class="kw">thus </span><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="c2">INS</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c5">k</font></span>)</span>)</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="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font> = 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7_1_1_2_8"><span class="lab"><font color="Green" title="E6">A23</font></span></a>, <a class="ref" href="scmring2.html#T16" title="SCMRING2:th.16">SCMRING2:16</a></span>
<br/>.= 
<font color="Maroon" title="c6">s</font> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</a></span>
<br/>.= 
<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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7_1_1_2_8"><span class="lab"><font color="Green" title="E7">A24</font></span></a>, <a class="ref" href="scmring2.html#T16" title="SCMRING2:th.16">SCMRING2:16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</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="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th7</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><span class="kw">hence </span><a NAME="E7:7_1_1_2_8"/>
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">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> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c2">INS</font>,<font color="Maroon" title="c3">j</font>)</span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c4">k</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7_1_1"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="scmring4.html#T6" target="_self" title="SCMRING4:th.6">Th8</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>
