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<span class="kw">let </span><font color="Maroon" title="c1">j</font>, <font color="Maroon" title="c2">k</font> be   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">R</font> being  <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a>  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a><br/> for <font color="Olive" title="b2">I</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b1">R</font></span>)</span><br/> for <font color="Olive" title="b3">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b1">R</font></span>)</span>  st  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Olive" title="b3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b1">R</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span> holds <br/> <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b2">I</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Olive" title="b3">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b1">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b1">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Olive" title="b2">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b3">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Olive" title="b2">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b3">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b1">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b1">R</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">R</font> be   <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a>  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">I</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span><br/> for <font color="Olive" title="b2">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>  st  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Olive" title="b2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span> holds <br/> <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b1">I</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Olive" title="b2">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Olive" title="b1">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Olive" title="b1">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b2">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">I</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>  st  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span> holds <br/> <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b1">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b1">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span> implies  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> )</span><br/>









<div><span class="lab"><font color="Green" title="E12">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c6">d</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c6">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<br/>.= 
<font color="Maroon" title="c5">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T112" title="AMI_1:th.112">AMI_1:112</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T112" title="AMI_1:th.112">AMI_1:112</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:22"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span><br/>

<span class="kw">then </span><span class="lab"><font color="Green" title="E14">A3</font></span>:  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>,<font color="Maroon" title="c1">j</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">AMISTD_1:def 13</a></span>
<br/>.= 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>,<font color="Maroon" title="c1">j</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_1.html#T61" title="AMISTD_1:th.61">AMISTD_1:61</a></span>
<br/>.= 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T67" title="SCMRING3:th.67">SCMRING3:67</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c2">k</font>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_1.html#T61" title="AMISTD_1:th.61">AMISTD_1:61</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">AMISTD_1:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="scmring3.html#T67" title="SCMRING3:th.67">SCMRING3:67</a></span>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_3"><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="E1:22_3"/>
(  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</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#T32" title="NAT_1:th.32">NAT_1:32</a>, <a class="ref" href="scmring3.html#T71" title="SCMRING3:th.71">SCMRING3:71</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_3_1"><span class="kw">suppose </span></a><a NAME="E1:22_3_1"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:22_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A4</font></span>: 
<font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T16" title="SCMRING3:th.16">SCMRING3:16</a></span>;<br/><span class="kw">hence </span> <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> = 
<font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a></span>
<br/>.= 
<font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_3_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_3_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="22_3_2"><span class="kw">suppose </span></a><a NAME="E1:22_3_2"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">da</font>, <font color="Maroon" title="c7">db</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c3">R</font><span class="kw"> such that </span><br/><a NAME="E3:22_3_2"/><span class="lab"><font color="Green" title="E15">A5</font></span>: 
<font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">da</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">db</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/><a NAME="E4:22_3_2"/><span class="lab"><font color="Green" title="E16">A6</font></span>: 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">da</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">db</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_2"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="ref" href="amistd_2.html#T29" title="AMISTD_2:th.29">AMISTD_2:29</a></span>;<br/><a NAME="E5:22_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A7</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#T13" title="SCMRING2:th.13">SCMRING2:13</a></span>;<br/><div><span class="lab"><font color="Green" title="E18">A8</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_3_2_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="c3">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_3_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="E1:22_3_2_1_1"/>
( <font color="Maroon" title="c6">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d</font> or <font color="Maroon" title="c6">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_3_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:22_3_2_1_1_1"/><span class="lab"><font color="Green" title="E19">A9</font></span>: 
<font color="Maroon" title="c6">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">db</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_2"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="ref" href="scmring2.html#T13" title="SCMRING2:th.13">SCMRING2:13</a></span>
<br/>.= 
<font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">db</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_3_2"><span class="lab"><font color="Green" title="E16">A6</font></span></a>, <a class="txt" href="#E1:22_3_2_1_1_1"><span class="lab"><font color="Green" title="E19">A9</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="22_3_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:22_3_2_1_1_2"/><span class="lab"><font color="Green" title="E19">A10</font></span>: 
<font color="Maroon" title="c6">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_2"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="ref" href="scmring2.html#T13" title="SCMRING2:th.13">SCMRING2:13</a></span>
<br/>.= 
<font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_3_2"><span class="lab"><font color="Green" title="E16">A6</font></span></a>, <a class="txt" href="#E1:22_3_2_1_1_2"><span class="lab"><font color="Green" title="E19">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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_2"><span class="lab"><font color="Green" title="E15">A5</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="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E5:22_3_2"><span class="lab"><font color="Green" title="E17">A7</font></span></a>, <a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
;<br/><span class="kw">hence </span><a NAME="E8:22_3_2"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E6:22_3_2"><span class="lab"><font color="Green" title="E18">A8</font></span></a>, <a class="ref" href="scmring4.html#T21" target="_self" title="SCMRING4:th.21">Th21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="22_3_3"><span class="kw">suppose </span></a><a NAME="E1:22_3_3"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</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="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">da</font>, <font color="Maroon" title="c7">db</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c3">R</font><span class="kw"> such that </span><br/><a NAME="E3:22_3_3"/><span class="lab"><font color="Green" title="E15">A11</font></span>: 
<font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c6">da</font>,<font color="Maroon" title="c7">db</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="E4:22_3_3"/><span class="lab"><font color="Green" title="E16">A12</font></span>: 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c6">da</font>,<font color="Maroon" title="c7">db</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_3"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="amistd_2.html#T29" title="AMISTD_2:th.29">AMISTD_2:29</a></span>;<br/><a NAME="E5:22_3_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A13</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#T14" title="SCMRING2:th.14">SCMRING2:14</a></span>;<br/><div><span class="lab"><font color="Green" title="E18">A14</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_3_3_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="c3">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_3_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="E1:22_3_3_1_1"/>
( <font color="Maroon" title="c6">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d</font> or <font color="Maroon" title="c6">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_3_3_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:22_3_3_1_1_1"/><span class="lab"><font color="Green" title="E19">A15</font></span>: 
<font color="Maroon" title="c6">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c6">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"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_3"><span class="lab"><font color="Green" title="E15">A11</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="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c6">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"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c6">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="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_3_3"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="txt" href="#E1:22_3_3_1_1_1"><span class="lab"><font color="Green" title="E19">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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="22_3_3_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:22_3_3_1_1_2"/><span class="lab"><font color="Green" title="E19">A16</font></span>: 
<font color="Maroon" title="c6">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_3"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="scmring2.html#T14" title="SCMRING2:th.14">SCMRING2:14</a></span>
<br/>.= 
<font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_3_3"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="txt" href="#E1:22_3_3_1_1_2"><span class="lab"><font color="Green" title="E19">A16</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_3"><span class="lab"><font color="Green" title="E15">A11</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="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E5:22_3_3"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
;<br/><span class="kw">hence </span><a NAME="E8:22_3_3"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E6:22_3_3"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="ref" href="scmring4.html#T21" target="_self" title="SCMRING4:th.21">Th21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="22_3_4"><span class="kw">suppose </span></a><a NAME="E1:22_3_4"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</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="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">da</font>, <font color="Maroon" title="c7">db</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c3">R</font><span class="kw"> such that </span><br/><a NAME="E3:22_3_4"/><span class="lab"><font color="Green" title="E15">A17</font></span>: 
<font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K6" title="SCMRING2:func.6">SubFrom</a> <font color="Maroon" title="c6">da</font>,<font color="Maroon" title="c7">db</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="E4:22_3_4"/><span class="lab"><font color="Green" title="E16">A18</font></span>: 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K6" title="SCMRING2:func.6">SubFrom</a> <font color="Maroon" title="c6">da</font>,<font color="Maroon" title="c7">db</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_4"><span class="lab"><font color="Green" title="E15">A17</font></span></a>, <a class="ref" href="amistd_2.html#T29" title="AMISTD_2:th.29">AMISTD_2:29</a></span>;<br/><a NAME="E5:22_3_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A19</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#T15" title="SCMRING2:th.15">SCMRING2:15</a></span>;<br/><div><span class="lab"><font color="Green" title="E18">A20</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_3_4_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="c3">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_3_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="E1:22_3_4_1_1"/>
( <font color="Maroon" title="c6">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d</font> or <font color="Maroon" title="c6">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_3_4_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:22_3_4_1_1_1"/><span class="lab"><font color="Green" title="E19">A21</font></span>: 
<font color="Maroon" title="c6">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c6">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"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_4"><span class="lab"><font color="Green" title="E15">A17</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"><font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c6">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"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c6">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="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_3_4"><span class="lab"><font color="Green" title="E16">A18</font></span></a>, <a class="txt" href="#E1:22_3_4_1_1_1"><span class="lab"><font color="Green" title="E19">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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="22_3_4_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:22_3_4_1_1_2"/><span class="lab"><font color="Green" title="E19">A22</font></span>: 
<font color="Maroon" title="c6">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_4"><span class="lab"><font color="Green" title="E15">A17</font></span></a>, <a class="ref" href="scmring2.html#T15" title="SCMRING2:th.15">SCMRING2:15</a></span>
<br/>.= 
<font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_3_4"><span class="lab"><font color="Green" title="E16">A18</font></span></a>, <a class="txt" href="#E1:22_3_4_1_1_2"><span class="lab"><font color="Green" title="E19">A22</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_4"><span class="lab"><font color="Green" title="E15">A17</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="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E5:22_3_4"><span class="lab"><font color="Green" title="E17">A19</font></span></a>, <a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
;<br/><span class="kw">hence </span><a NAME="E8:22_3_4"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E6:22_3_4"><span class="lab"><font color="Green" title="E18">A20</font></span></a>, <a class="ref" href="scmring4.html#T21" target="_self" title="SCMRING4:th.21">Th21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="22_3_5"><span class="kw">suppose </span></a><a NAME="E1:22_3_5"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">da</font>, <font color="Maroon" title="c7">db</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c3">R</font><span class="kw"> such that </span><br/><a NAME="E3:22_3_5"/><span class="lab"><font color="Green" title="E15">A23</font></span>: 
<font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K7" title="SCMRING2:func.7">MultBy</a> <font color="Maroon" title="c6">da</font>,<font color="Maroon" title="c7">db</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T20" title="SCMRING3:th.20">SCMRING3:20</a></span>;<br/><a NAME="E4:22_3_5"/><span class="lab"><font color="Green" title="E16">A24</font></span>: 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K7" title="SCMRING2:func.7">MultBy</a> <font color="Maroon" title="c6">da</font>,<font color="Maroon" title="c7">db</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_5"><span class="lab"><font color="Green" title="E15">A23</font></span></a>, <a class="ref" href="amistd_2.html#T29" title="AMISTD_2:th.29">AMISTD_2:29</a></span>;<br/><a NAME="E5:22_3_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A25</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#T16" title="SCMRING2:th.16">SCMRING2:16</a></span>;<br/><div><span class="lab"><font color="Green" title="E18">A26</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_3_5_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="c3">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_3_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="E1:22_3_5_1_1"/>
( <font color="Maroon" title="c6">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d</font> or <font color="Maroon" title="c6">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_3_5_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:22_3_5_1_1_1"/><span class="lab"><font color="Green" title="E19">A27</font></span>: 
<font color="Maroon" title="c6">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c6">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"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_5"><span class="lab"><font color="Green" title="E15">A23</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"><font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c6">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"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c6">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="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_3_5"><span class="lab"><font color="Green" title="E16">A24</font></span></a>, <a class="txt" href="#E1:22_3_5_1_1_1"><span class="lab"><font color="Green" title="E19">A27</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="22_3_5_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:22_3_5_1_1_2"/><span class="lab"><font color="Green" title="E19">A28</font></span>: 
<font color="Maroon" title="c6">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_5"><span class="lab"><font color="Green" title="E15">A23</font></span></a>, <a class="ref" href="scmring2.html#T16" title="SCMRING2:th.16">SCMRING2:16</a></span>
<br/>.= 
<font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_3_5"><span class="lab"><font color="Green" title="E16">A24</font></span></a>, <a class="txt" href="#E1:22_3_5_1_1_2"><span class="lab"><font color="Green" title="E19">A28</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_5"><span class="lab"><font color="Green" title="E15">A23</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="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E5:22_3_5"><span class="lab"><font color="Green" title="E17">A25</font></span></a>, <a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
;<br/><span class="kw">hence </span><a NAME="E8:22_3_5"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E6:22_3_5"><span class="lab"><font color="Green" title="E18">A26</font></span></a>, <a class="ref" href="scmring4.html#T21" target="_self" title="SCMRING4:th.21">Th21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="22_3_6"><span class="kw">suppose </span></a><a NAME="E1:22_3_6"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">da</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c3">R</font>, <font color="Maroon" title="c7">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">R</font><span class="kw"> such that </span><br/><a NAME="E3:22_3_6"/><span class="lab"><font color="Green" title="E15">A29</font></span>: 
<font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">da</font> <a href="scmring2.html#K8" title="SCMRING2:func.8">:=</a> <font color="Maroon" title="c7">r</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T21" title="SCMRING3:th.21">SCMRING3:21</a></span>;<br/><a NAME="E4:22_3_6"/><span class="lab"><font color="Green" title="E16">A30</font></span>: 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">da</font> <a href="scmring2.html#K8" title="SCMRING2:func.8">:=</a> <font color="Maroon" title="c7">r</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_6"><span class="lab"><font color="Green" title="E15">A29</font></span></a>, <a class="ref" href="amistd_2.html#T29" title="AMISTD_2:th.29">AMISTD_2:29</a></span>;<br/><a NAME="E5:22_3_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A31</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#T19" title="SCMRING2:th.19">SCMRING2:19</a></span>;<br/><div><span class="lab"><font color="Green" title="E18">A32</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_3_6_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="c3">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_3_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="E1:22_3_6_1_1"/>
( <font color="Maroon" title="c6">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d</font> or <font color="Maroon" title="c6">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_3_6_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:22_3_6_1_1_1"/><span class="lab"><font color="Green" title="E19">A33</font></span>: 
<font color="Maroon" title="c6">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font> = 
<font color="Maroon" title="c7">r</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_6"><span class="lab"><font color="Green" title="E15">A29</font></span></a>, <a class="ref" href="scmring2.html#T19" title="SCMRING2:th.19">SCMRING2:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_3_6"><span class="lab"><font color="Green" title="E16">A30</font></span></a>, <a class="txt" href="#E1:22_3_6_1_1_1"><span class="lab"><font color="Green" title="E19">A33</font></span></a>, <a class="ref" href="scmring2.html#T19" title="SCMRING2:th.19">SCMRING2:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="22_3_6_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:22_3_6_1_1_2"/><span class="lab"><font color="Green" title="E19">A34</font></span>: 
<font color="Maroon" title="c6">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_6"><span class="lab"><font color="Green" title="E15">A29</font></span></a>, <a class="ref" href="scmring2.html#T19" title="SCMRING2:th.19">SCMRING2:19</a></span>
<br/>.= 
<font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_3_6"><span class="lab"><font color="Green" title="E16">A30</font></span></a>, <a class="txt" href="#E1:22_3_6_1_1_2"><span class="lab"><font color="Green" title="E19">A34</font></span></a>, <a class="ref" href="scmring2.html#T19" title="SCMRING2:th.19">SCMRING2:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_6"><span class="lab"><font color="Green" title="E15">A29</font></span></a>, <a class="ref" href="scmring2.html#T19" title="SCMRING2:th.19">SCMRING2:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E5:22_3_6"><span class="lab"><font color="Green" title="E17">A31</font></span></a>, <a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
;<br/><span class="kw">hence </span><a NAME="E8:22_3_6"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E6:22_3_6"><span class="lab"><font color="Green" title="E18">A32</font></span></a>, <a class="ref" href="scmring4.html#T21" target="_self" title="SCMRING4:th.21">Th21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="22_3_7"><span class="kw">suppose </span></a><a NAME="E1:22_3_7"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">loc</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:22_3_7"/><span class="lab"><font color="Green" title="E15">A35</font></span>: 
<font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c6">loc</font>,<font color="Maroon" title="c3">R</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T22" title="SCMRING3:th.22">SCMRING3:22</a></span>;<br/><a NAME="E4:22_3_7"/><span class="lab"><font color="Green" title="E16">A36</font></span>: 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">loc</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c2">k</font>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_7"><span class="lab"><font color="Green" title="E15">A35</font></span></a>, <a class="ref" href="scmring3.html#T69" title="SCMRING3:th.69">SCMRING3:69</a></span>;<br/><a NAME="E5:22_3_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A37</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">loc</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c2">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#T17" title="SCMRING2:th.17">SCMRING2:17</a></span>;<br/><div><span class="lab"><font color="Green" title="E18">A38</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_3_7_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">d</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c3">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">d</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_7"><span class="lab"><font color="Green" title="E15">A35</font></span></a>, <a class="ref" href="scmring2.html#T17" title="SCMRING2:th.17">SCMRING2:17</a></span>
<br/>.= 
<font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_3_7"><span class="lab"><font color="Green" title="E16">A36</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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<font color="Maroon" title="c6">loc</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_7"><span class="lab"><font color="Green" title="E15">A35</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="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22_3_7"><span class="lab"><font color="Green" title="E17">A37</font></span></a>, <a class="ref" href="amistd_1.html#T61" title="AMISTD_1:th.61">AMISTD_1:61</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
;<br/><span class="kw">hence </span><a NAME="E8:22_3_7"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E6:22_3_7"><span class="lab"><font color="Green" title="E18">A38</font></span></a>, <a class="ref" href="scmring4.html#T21" target="_self" title="SCMRING4:th.21">Th21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="22_3_8"><span class="kw">suppose </span></a><a NAME="E1:22_3_8"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</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="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">da</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c3">R</font>, <font color="Maroon" title="c7">loc</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:22_3_8"/><span class="lab"><font color="Green" title="E15">A39</font></span>: 
<font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">da</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c7">loc</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T23" title="SCMRING3:th.23">SCMRING3:23</a></span>;<br/><a NAME="E4:22_3_8"/><span class="lab"><font color="Green" title="E16">A40</font></span>: 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">da</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">loc</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c2">k</font>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_8"><span class="lab"><font color="Green" title="E15">A39</font></span></a>, <a class="ref" href="scmring3.html#T70" title="SCMRING3:th.70">SCMRING3:70</a></span>;<br/><div><span class="lab"><font color="Green" title="E17">A41</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_3_8_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_3_8_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="E1:22_3_8_1_1"/>
( <font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c6">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">R</font> or <font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c6">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">R</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_3_8_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:22_3_8_1_1_1"/><span class="lab"><font color="Green" title="E18">A42</font></span>: 
<font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c6">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">R</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:22_3_8_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A43</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">loc</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c2">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_3_8"><span class="lab"><font color="Green" title="E16">A40</font></span></a>, <a class="ref" href="scmring2.html#T18" title="SCMRING2:th.18">SCMRING2:18</a></span>;<br/><a NAME="E3:22_3_8_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c6">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_3_8_1_1_1"><span class="lab"><font color="Green" title="E18">A42</font></span></a>, <a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>;<br/><span class="kw">then </span> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<font color="Maroon" title="c7">loc</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_8"><span class="lab"><font color="Green" title="E15">A39</font></span></a>, <a class="ref" href="scmring2.html#T18" title="SCMRING2:th.18">SCMRING2:18</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_3_8_1_1_1"><span class="lab"><font color="Green" title="E19">A43</font></span></a>, <a class="ref" href="amistd_1.html#T61" title="AMISTD_1:th.61">AMISTD_1:61</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
;<br/><span class="kw">hence </span><a NAME="E5:22_3_8_1_1_1"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="22_3_8_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:22_3_8_1_1_2"/><span class="lab"><font color="Green" title="E18">A44</font></span>: 
<font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c6">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">R</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:22_3_8_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A45</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_3_8"><span class="lab"><font color="Green" title="E16">A40</font></span></a>, <a class="ref" href="scmring2.html#T18" title="SCMRING2:th.18">SCMRING2:18</a></span>;<br/><a NAME="E3:22_3_8_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c6">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_3_8_1_1_2"><span class="lab"><font color="Green" title="E18">A44</font></span></a>, <a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>;<br/><span class="kw">then </span> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_8"><span class="lab"><font color="Green" title="E15">A39</font></span></a>, <a class="ref" href="scmring2.html#T18" title="SCMRING2:th.18">SCMRING2:18</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E2:22_3_8_1_1_2"><span class="lab"><font color="Green" title="E19">A45</font></span></a>, <a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
;<br/><span class="kw">hence </span><a NAME="E5:22_3_8_1_1_2"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_3_8_2"><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="c3">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p5">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3_8"><span class="lab"><font color="Green" title="E15">A39</font></span></a>, <a class="ref" href="scmring2.html#T18" title="SCMRING2:th.18">SCMRING2:18</a></span>
<br/>.= 
<font color="Maroon" title="c5">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_3_8"><span class="lab"><font color="Green" title="E16">A40</font></span></a>, <a class="ref" href="scmring2.html#T18" title="SCMRING2:th.18">SCMRING2:18</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E7:22_3_8"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c5">s</font></span>)</span></span>)</span> <a href="amistd_1.html#K11" title="AMISTD_1:func.11">-'</a> <font color="Maroon" title="c2">k</font>,<span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E5:22_3_8"><span class="lab"><font color="Green" title="E17">A41</font></span></a>, <a class="ref" href="scmring4.html#T21" target="_self" title="SCMRING4:th.21">Th21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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>
