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<span class="kw">let </span><font color="Maroon" title="c3">i</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</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">s</font> being  <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> <br/> for <font color="Olive" title="b2">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>  holds   <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="Olive" title="b1">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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Olive" title="b2">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Olive" title="b2">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">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>  holds   <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="c4">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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">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">  <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="c4">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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i</font></span><br/>





<span class="kw">set </span><font color="Maroon" title="c6">iI</font> = <font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">IsiI</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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">s3</font> = <font color="Maroon" title="c4">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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>;<br/>
<a NAME="E1:21"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <font color="Maroon" title="c3">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T2" title="SCMPDS_5:th.2">SCMPDS_5:2</a></span>;<br/>
<a NAME="E2:21"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">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="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T15" target="_self" title="SCMPDS_6:th.15">Th15</a></span>;<br/>
<a NAME="E3:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A2</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<a NAME="E4:21"/><span class="lab"><font color="Green" title="E21">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"><font color="Maroon" title="c4">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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span></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"><font color="Maroon" title="c4">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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span></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"><font color="Maroon" title="c4">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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span></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="E5:21"/>
<font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T17" target="_self" title="SCMPDS_6:th.17">Th17</a></span>;<br/>
<a NAME="E6:21"/><span class="kw">then </span>
 <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c4">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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:21"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:21"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="scmpds_6.html#T20" target="_self" title="SCMPDS_6:th.20">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.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_4.html#D4" title="SCMPDS_4:def.4">SCMPDS_4:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="scmpds_4.html#T37" title="SCMPDS_4:th.37">SCMPDS_4:37</a></span>
<br/>.= 
<font color="Maroon" title="c3">i</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T4" title="SCMPDS_5:th.4">SCMPDS_5:4</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:21"/>
 <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="c4">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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">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"><font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:21"><span class="lab"><font color="Green" title="E21">Y</font></span></a>, <a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a>, <a class="ref" href="scmpds_5.html#T18" title="SCMPDS_5:th.18">SCMPDS_5:18</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>
