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<span class="kw">let </span><font color="Maroon" title="c3">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">I</font> being  <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> <br/> for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">c</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> <br/> for <font color="Olive" title="b4">i</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><br/> for <font color="Olive" title="b5">n</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>   st <font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b2">a</font></span>)</span>,<font color="Olive" title="b4">i</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">i</font>,<font color="Olive" title="b5">n</font>,<font color="Olive" title="b1">I</font></span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">I</font> be   <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">c</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> <br/> for <font color="Olive" title="b3">i</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><br/> for <font color="Olive" title="b4">n</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>   st <font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b1">a</font></span>)</span>,<font color="Olive" title="b3">i</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">i</font>,<font color="Olive" title="b4">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">i</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><br/> for <font color="Olive" title="b2">n</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>   st <font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Olive" title="b1">i</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c7">i</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</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">n</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>   st <font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c7">i</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Olive" title="b1">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c8">n</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"> ( <font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c7">i</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span> )</span><br/>









<span class="kw">set </span><font color="Maroon" title="c9">d1</font> =  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c7">i</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">FOR</font> =  <a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">pFOR</font> =  <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">iFOR</font> =  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">s3</font> = <font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">s4</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,1;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">i1</font> = <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">i2</font> =  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">i3</font> =  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c18">SAl</font> =  <a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/>
<a NAME="E1:55"/><span class="lab"><font color="Green" title="E43">A1</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T21" title="SCMPDS_6:th.21">SCMPDS_6:21</a></span>;<br/>
<a NAME="E2:55"/><span class="lab"><font color="Green" title="E44">A2</font></span>: 
not  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T31" title="SCMPDS_4:th.31">SCMPDS_4:31</a></span>;<br/>
<a NAME="E3:55"/>
 <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></span>;<br/>
<a NAME="E4:55"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A3</font></span>: 
 <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T81" title="AMI_1:th.81">AMI_1:81</a>, <a class="ref" href="scmpds_4.html#T57" title="SCMPDS_4:th.57">SCMPDS_4:57</a></span>;<br/>
<a NAME="E5:55"/>
not <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T31" title="SCMPDS_4:th.31">SCMPDS_4:31</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E46">A4</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c7">i</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c7">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c7">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E44">A2</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>
;<br/>
<a NAME="E7:55"/><span class="lab"><font color="Green" title="E47">A5</font></span>: 
 <a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_7.html#T15" target="_self" title="SCMPDS_7:th.15">Th15</a></span>;<br/>
<span class="lab"><font color="Green" title="E48">A6</font></span>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></span>
<br/>.= 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:55"><span class="lab"><font color="Green" title="E47">A5</font></span></a>, <a class="ref" href="scmpds_6.html#T22" title="SCMPDS_6:th.22">SCMPDS_6:22</a></span>
;<br/>
<span class="kw">assume </span><a NAME="E9:55"/>
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c7">i</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</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="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span><br/>

<span class="kw">then </span><span class="lab"><font color="Green" title="E49">A7</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#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:55"><span class="lab"><font color="Green" title="E48">A6</font></span></a>, <a class="txt" href="#E6:55"><span class="lab"><font color="Green" title="E46">A4</font></span></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></span>
<br/>.= 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="ref" href="scmpds_6.html#T23" title="SCMPDS_6:th.23">SCMPDS_6:23</a></span>
;<br/>
<a NAME="E11:55"/><span class="lab"><font color="Green" title="E50">Y</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</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"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,1</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#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</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"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T150" title="AMI_1:th.150">AMI_1:150</a></span>;<br/>
<a NAME="E12:55"/><span class="lab"><font color="Green" title="E51">TX</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/>
<a NAME="E13:55"/><span class="lab"><font color="Green" title="E52">A8</font></span>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_7.html#T51" target="_self" title="SCMPDS_7:th.51">Th51</a></span>;<br/>
<a NAME="E14:55"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T25" title="SCMPDS_6:th.25">SCMPDS_6:25</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:55"><span class="lab"><font color="Green" title="E45">A3</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
<br/>.= 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:55"><span class="lab"><font color="Green" title="E52">A8</font></span></a>, <a class="ref" href="scmpds_6.html#T25" title="SCMPDS_6:th.25">SCMPDS_6:25</a></span>
;<br/>
<a NAME="E16:55"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A9</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:55"><span class="lab"><font color="Green" title="E49">A7</font></span></a>, <a class="txt" href="#E11:55"><span class="lab"><font color="Green" title="E50">Y</font></span></a></span>;<br/>
<a NAME="E17:55"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A10</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:55"><span class="lab"><font color="Green" title="E51">TX</font></span></a>, <a class="ref" href="ami_1.html#T146" title="AMI_1:th.146">AMI_1:146</a></span>;<br/>
<a NAME="E18:55"/><span class="lab"><font color="Green" title="E55">A11</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:55"><span class="lab"><font color="Green" title="E47">A5</font></span></a>, <a class="ref" href="scmpds_6.html#T22" title="SCMPDS_6:th.22">SCMPDS_6:22</a></span>;<br/>
<a NAME="E19:55"/><span class="lab"><font color="Green" title="E56">TX</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_5"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">l</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"> ( <font color="Maroon" title="c19">l</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 implies  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c19">l</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  )</span><br/><a NAME="E1:55_5"/><span class="lab"><font color="Green" title="E57">u</font></span>: 
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>;<br/><span class="kw">assume </span><a NAME="E2:55_5"/>
<font color="Maroon" title="c19">l</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</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#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c19">l</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span><br/><a NAME="E3:55_5"/><span class="kw">then </span>
<font color="Maroon" title="c19">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E4:55_5"/><span class="kw">then </span>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c19">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55_5"><span class="lab"><font color="Green" title="E57">u</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:55_5"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c19">l</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:55"><span class="lab"><font color="Green" title="E55">A11</font></span></a>, <a class="ref" href="scmpds_6.html#T31" title="SCMPDS_6:th.31">SCMPDS_6:31</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 NAME="E21:55"/><span class="kw">then </span>
for <font color="Olive" title="b1">l</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>   st  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive" title="b1">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  holds <br/>1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">l</font>
 
;<br/>
<a NAME="E22:55"/><span class="kw">then </span>
 <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:55"><span class="lab"><font color="Green" title="E53">A9</font></span></a>, <a class="txt" href="#E17:55"><span class="lab"><font color="Green" title="E54">A10</font></span></a>, <a class="txt" href="#E19:55"><span class="lab"><font color="Green" title="E56">TX</font></span></a>, <a class="ref" href="ami_1.html#D46" title="AMI_1:def.46">AMI_1:def 46</a></span>;<br/>
<a NAME="E23:55"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A12</font></span>: 
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:55"><span class="lab"><font color="Green" title="E54">A10</font></span></a>, <a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a></span>;<br/>
<a NAME="E24:55"/><span class="lab"><font color="Green" title="E58">A13</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T143" title="AMI_1:th.143">AMI_1:143</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E59">A14</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="55_6"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> implies <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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"><font color="Maroon" title="c3">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><a NAME="E1:55_6"/><span class="lab"><font color="Green" title="E60">A15</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/><span class="kw">assume </span><a NAME="E2:55_6"/><span class="lab"><font color="Green" title="E61">A16</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span>
 ; <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="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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"><font color="Maroon" title="c3">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_6_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:55_6_1"/>
( <font color="Maroon" title="c19">x</font> is    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  or <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  or <font color="Maroon" title="c19">x</font> is    <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><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:55_6"><span class="lab"><font color="Green" title="E61">A16</font></span></a>, <a class="ref" href="scmpds_4.html#T20" title="SCMPDS_4:th.20">SCMPDS_4:20</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_6_1_1"><span class="kw">suppose </span></a><a NAME="E1:55_6_1_1"/><span class="lab"><font color="Green" title="E62">A17</font></span>: 
<font color="Maroon" title="c19">x</font> is    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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"><font color="Maroon" title="c3">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:55_6_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T52" title="SCMPDS_2:th.52">SCMPDS_2:52</a></span>;<br/><a NAME="E3:55_6_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A18</font></span>: 
not <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55_6"><span class="lab"><font color="Green" title="E60">A15</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E4:55_6_1_1"/>
not <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:55"><span class="lab"><font color="Green" title="E58">A13</font></span></a>, <a class="txt" href="#E1:55_6_1_1"><span class="lab"><font color="Green" title="E62">A17</font></span></a>, <a class="ref" href="scmpds_2.html#T53" title="SCMPDS_2:th.53">SCMPDS_2:53</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:55"><span class="lab"><font color="Green" title="E57">A12</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:55"><span class="lab"><font color="Green" title="E48">A6</font></span></a>, <a class="txt" href="#E1:55_6_1_1"><span class="lab"><font color="Green" title="E62">A17</font></span></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></span>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55_6_1_1"><span class="lab"><font color="Green" title="E62">A17</font></span></a>, <a class="ref" href="scmpds_5.html#T19" title="SCMPDS_5:th.19">SCMPDS_5:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:55_6_1_1"><span class="lab"><font color="Green" title="E63">A18</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</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="55_6_1_2"><span class="kw">suppose </span></a><a NAME="E1:55_6_1_2"/><span class="lab"><font color="Green" title="E62">A19</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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"><font color="Maroon" title="c3">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:55_6_1_2"/>
not <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:55"><span class="lab"><font color="Green" title="E58">A13</font></span></a>, <a class="txt" href="#E1:55_6_1_2"><span class="lab"><font color="Green" title="E62">A19</font></span></a>, <a class="ref" href="ami_1.html#T48" title="AMI_1:th.48">AMI_1:48</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> = 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:55"><span class="lab"><font color="Green" title="E49">A7</font></span></a>, <a class="txt" href="#E23:55"><span class="lab"><font color="Green" title="E57">A12</font></span></a>, <a class="txt" href="#E1:55_6_1_2"><span class="lab"><font color="Green" title="E62">A19</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55_6_1_2"><span class="lab"><font color="Green" title="E62">A19</font></span></a>, <a class="ref" href="scmpds_7.html#T12" target="_self" title="SCMPDS_7:th.12">Th12</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="55_6_1_3"><span class="kw">suppose </span></a><a NAME="E1:55_6_1_3"/>
<font color="Maroon" title="c19">x</font> is    <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="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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"><font color="Maroon" title="c3">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:55_6_1_3"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T27" title="SCMPDS_6:th.27">SCMPDS_6:27</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><span class="kw">end;</span></div>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> = 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E27:55"/>
 <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:55"><span class="lab"><font color="Green" title="E59">A14</font></span></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</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>
