let s be State of SCM+FSA; :: thesis: for c being read-write Int-Location
for aa, bb being Int-Location
for f being FinSeq-Location
for p being Instruction-Sequence of SCM+FSA st aa <> c & bb <> c & s . (intloc 0) = 1 holds
( (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . f = s . f & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . aa = s . aa & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . bb = s . bb )
let c be read-write Int-Location; :: thesis: for aa, bb being Int-Location
for f being FinSeq-Location
for p being Instruction-Sequence of SCM+FSA st aa <> c & bb <> c & s . (intloc 0) = 1 holds
( (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . f = s . f & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . aa = s . aa & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . bb = s . bb )
let aa, bb be Int-Location; :: thesis: for f being FinSeq-Location
for p being Instruction-Sequence of SCM+FSA st aa <> c & bb <> c & s . (intloc 0) = 1 holds
( (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . f = s . f & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . aa = s . aa & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . bb = s . bb )
let f be FinSeq-Location ; :: thesis: for p being Instruction-Sequence of SCM+FSA st aa <> c & bb <> c & s . (intloc 0) = 1 holds
( (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . f = s . f & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . aa = s . aa & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . bb = s . bb )
let p be Instruction-Sequence of SCM+FSA; :: thesis: ( aa <> c & bb <> c & s . (intloc 0) = 1 implies ( (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . f = s . f & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . aa = s . aa & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . bb = s . bb ) )
assume that
A1: aa <> c and
A2: bb <> c and
A3: s . (intloc 0) = 1 ; :: thesis: ( (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . f = s . f & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . aa = s . aa & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . bb = s . bb )
set a = aa;
set b = bb;
set i0 = c := aa;
set s1 = Exec ((c := aa),(Initialized s));
set p1 = p;
A4: ( aa = intloc 0 or aa is read-write ) by SCMFSA_M:def 2;
A5: ( bb = intloc 0 or bb is read-write ) by SCMFSA_M:def 2;
A6: (Exec ((c := aa),(Initialized s))) . bb = (Initialized s) . bb by A2, SCMFSA_2:63
.= s . bb by A3, A5, SCMFSA_M:9, SCMFSA_M:37 ;
set cv = 3 -rdRWNotIn {aa,bb,c};
set aux2 = 2 -ndRWNotIn {aa,bb,c};
set aux1 = 1 -stRWNotIn {aa,bb,c};
set i10 = (1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}));
set i11 = (2 -ndRWNotIn {aa,bb,c}) := (f,c);
set I12 = if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA));
set I1B = (((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)));
set I1 = for-up ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))));
A7: 2 -ndRWNotIn {aa,bb,c} <> 3 -rdRWNotIn {aa,bb,c} by SCMFSA_M:26;
3 -rdRWNotIn {aa,bb,c} in {(3 -rdRWNotIn {aa,bb,c}),aa,bb} by ENUMSET1:def 1;
then A8: 3 -rdRWNotIn {aa,bb,c} in {(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))) by XBOOLE_0:def 3;
A9: 1 -stRWNotIn {aa,bb,c} <> 3 -rdRWNotIn {aa,bb,c} by SCMFSA_M:26;
A10: bb in {aa,bb,c} by ENUMSET1:def 1;
then A11: 3 -rdRWNotIn {aa,bb,c} <> bb by SCMFSA_M:25;
A12: 1 -stRWNotIn {aa,bb,c} <> bb by A10, SCMFSA_M:25;
A13: 2 -ndRWNotIn {aa,bb,c} <> bb by A10, SCMFSA_M:25;
A14: (Exec ((c := aa),(Initialized s))) . aa = (Initialized s) . aa by A1, SCMFSA_2:63
.= s . aa by A3, A4, SCMFSA_M:9, SCMFSA_M:37 ;
bb in {(3 -rdRWNotIn {aa,bb,c}),aa,bb} by ENUMSET1:def 1;
then A15: bb in {(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))) by XBOOLE_0:def 3;
A16: aa in {aa,bb,c} by ENUMSET1:def 1;
then A17: 3 -rdRWNotIn {aa,bb,c} <> aa by SCMFSA_M:25;
A18: 1 -stRWNotIn {aa,bb,c} <> aa by A16, SCMFSA_M:25;
A19: 2 -ndRWNotIn {aa,bb,c} <> aa by A16, SCMFSA_M:25;
A20: (Exec ((c := aa),(Initialized s))) . f = (Initialized s) . f by SCMFSA_2:63
.= s . f by SCMFSA_M:37 ;
aa in {(3 -rdRWNotIn {aa,bb,c}),aa,bb} by ENUMSET1:def 1;
then A21: aa in {(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))) by XBOOLE_0:def 3;
c in {aa,bb,c} by ENUMSET1:def 1;
then A22: 3 -rdRWNotIn {aa,bb,c} <> c by SCMFSA_M:25;
A23: (Exec ((c := aa),(Initialized s))) . (intloc 0) = (Initialized s) . (intloc 0) by SCMFSA_2:63
.= 1 by SCMFSA_M:9 ;
then A24: for-up ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))) is_halting_on Exec ((c := aa),(Initialized s)),p by Th24;

per cases ( s . aa > s . bb or s . aa <= s . bb ) ;

suppose A25: s . aa > s . bb ; :: thesis: ( (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . f = s . f & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . aa = s . aa & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . bb = s . bb )

thus (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . f = (IExec ((for-up ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))))),p,(Exec ((c := aa),(Initialized s))))) . f by A24, SFMASTR1:15
.= s . f by A23, A14, A6, A20, A25, Th22 ; :: thesis: ( (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . aa = s . aa & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . bb = s . bb )
aa in {aa,bb} by TARSKI:def 2;
then A26: aa in {aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))) by XBOOLE_0:def 3;
thus (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . aa = (IExec ((for-up ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))))),p,(Exec ((c := aa),(Initialized s))))) . aa by A24, SFMASTR1:14
.= s . aa by A17, A23, A14, A6, A25, A26, Th22 ; :: thesis: (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . bb = s . bb
bb in {aa,bb} by TARSKI:def 2;
then A27: bb in {aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))) by XBOOLE_0:def 3;
thus (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . bb = (IExec ((for-up ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))))),p,(Exec ((c := aa),(Initialized s))))) . bb by A24, SFMASTR1:14
.= s . bb by A11, A23, A14, A6, A25, A27, Th22 ; :: thesis: verum

end;

suppose A28: s . aa <= s . bb ; :: thesis: ( (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . f = s . f & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . aa = s . aa & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . bb = s . bb )

set SF = StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))));
A29: (s . aa) - (s . aa) <= (s . bb) - (s . aa) by A28, XREAL_1:9;
then reconsider k = ((s . bb) - (s . aa)) + 1 as Element of NAT by INT_1:3;
defpred S₁[ Nat] means ( 0 < $1 & $1 <= k implies ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . $1) . (intloc 0) = 1 & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . $1) . (3 -rdRWNotIn {aa,bb,c}) = $1 + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . $1) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . $1) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . $1) . bb = (Exec ((c := aa),(Initialized s))) . bb ) );
A30: ProperForUpBody 3 -rdRWNotIn {aa,bb,c},aa,bb,(((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))), Exec ((c := aa),(Initialized s)),p by Th15;
A31: for n being Nat st S₁[n] holds
S₁[n + 1]

proof

let n be Nat; :: thesis: ( S₁[n] implies S₁[n + 1] )
assume that
A32: S₁[n] and
0 < n + 1 and
A33: n + 1 <= k ; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (intloc 0) = 1 & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )
A34: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (intloc 0) = 1 & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) = n + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) <= (Exec ((c := aa),(Initialized s))) . bb )

proof

per cases ( 0 = n or 0 < n ) ;

suppose A35: 0 = n ; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (intloc 0) = 1 & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) = n + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) <= (Exec ((c := aa),(Initialized s))) . bb )

hence ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (intloc 0) = 1 by A23, Th8; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) = n + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) <= (Exec ((c := aa),(Initialized s))) . bb )
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) = n + ((Exec ((c := aa),(Initialized s))) . aa) by A35, Th9; :: thesis: ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) <= (Exec ((c := aa),(Initialized s))) . bb
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) <= (Exec ((c := aa),(Initialized s))) . bb by A14, A6, A28, A35, Th9; :: thesis: verum

end;

suppose A36: 0 < n ; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (intloc 0) = 1 & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) = n + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) <= (Exec ((c := aa),(Initialized s))) . bb )

hence ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (intloc 0) = 1 by A32, A33, NAT_1:13; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) = n + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) <= (Exec ((c := aa),(Initialized s))) . bb )
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) = n + ((Exec ((c := aa),(Initialized s))) . aa) by A32, A33, A36, NAT_1:13; :: thesis: ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) <= (Exec ((c := aa),(Initialized s))) . bb
(n + 1) - 1 <= (((s . bb) - (s . aa)) + 1) - 1 by A33, XREAL_1:9;
hence ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) <= (Exec ((c := aa),(Initialized s))) . bb by A14, A6, A32, A33, A36, NAT_1:13, XREAL_1:19; :: thesis: verum

end;

end;

end;

n < n + 1 by XREAL_1:29;
then n < k by A33, XXREAL_0:2;
then A37: ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) | (({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))))) \/ FinSeq-Locations) = (IExec ((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) | (({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))))) \/ FinSeq-Locations) by A23, A14, A6, A30, Th19;
then A38: ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (IExec ((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . f by SCMFSA_M:28
.= (Exec ((AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0))),(IExec (((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . f by SFMASTR1:12
.= (IExec (((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . f by SCMFSA_2:64
.= (IExec ((if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . f by SFMASTR1:8 ;
A39: ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (IExec ((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . bb by A15, A37, SCMFSA_M:28
.= (Exec ((AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0))),(IExec (((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . bb by SFMASTR1:11
.= (IExec (((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . bb by A11, SCMFSA_2:64
.= (IExec ((if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . bb by SFMASTR1:7 ;
A40: ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (IExec ((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . aa by A21, A37, SCMFSA_M:28
.= (Exec ((AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0))),(IExec (((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . aa by SFMASTR1:11
.= (IExec (((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . aa by A17, SCMFSA_2:64
.= (IExec ((if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . aa by SFMASTR1:7 ;
A41: ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = (IExec ((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (3 -rdRWNotIn {aa,bb,c}) by A8, A37, SCMFSA_M:28
.= (Exec ((AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0))),(IExec (((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . (3 -rdRWNotIn {aa,bb,c}) by SFMASTR1:11
.= ((IExec (((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (3 -rdRWNotIn {aa,bb,c})) + ((IExec (((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (intloc 0)) by SCMFSA_2:64
.= ((IExec (((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (3 -rdRWNotIn {aa,bb,c})) + 1 by SCMFSA6B:11
.= ((IExec ((if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . (3 -rdRWNotIn {aa,bb,c})) + 1 by SFMASTR1:7 ;
set ss = IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n));
set S0 = Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n);
set S1 = Exec (((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))),(Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)));
set S2 = Exec (((2 -ndRWNotIn {aa,bb,c}) := (f,c)),(Exec (((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))),(Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))));
A42: (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . f = (Exec (((2 -ndRWNotIn {aa,bb,c}) := (f,c)),(Exec (((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))),(Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))))) . f by SCMFSA6C:9
.= (Exec (((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))),(Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))) . f by SCMFSA_2:72
.= (Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)) . f by SCMFSA_2:72 ;
A43: (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (intloc 0) = (Exec (((2 -ndRWNotIn {aa,bb,c}) := (f,c)),(Exec (((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))),(Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))))) . (intloc 0) by SCMFSA6C:8
.= (Exec (((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))),(Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))) . (intloc 0) by SCMFSA_2:72
.= (Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)) . (intloc 0) by SCMFSA_2:72
.= 1 by SCMFSA_M:9 ;
then A44: DataPart (IExec ((Stop SCM+FSA),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) = DataPart (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) by Th1;
A45: (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . bb = (Exec (((2 -ndRWNotIn {aa,bb,c}) := (f,c)),(Exec (((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))),(Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))))) . bb by SCMFSA6C:8
.= (Exec (((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))),(Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))) . bb by A13, SCMFSA_2:72
.= (Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)) . bb by A12, SCMFSA_2:72 ;
A46: (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . aa = (Exec (((2 -ndRWNotIn {aa,bb,c}) := (f,c)),(Exec (((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))),(Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))))) . aa by SCMFSA6C:8
.= (Exec (((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))),(Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))) . aa by A19, SCMFSA_2:72
.= (Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)) . aa by A18, SCMFSA_2:72 ;
A47: (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (3 -rdRWNotIn {aa,bb,c}) = (Exec (((2 -ndRWNotIn {aa,bb,c}) := (f,c)),(Exec (((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))),(Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))))) . (3 -rdRWNotIn {aa,bb,c}) by SCMFSA6C:8
.= (Exec (((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))),(Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))) . (3 -rdRWNotIn {aa,bb,c}) by A7, SCMFSA_2:72
.= (Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)) . (3 -rdRWNotIn {aa,bb,c}) by A9, SCMFSA_2:72 ;
A48: ( not Macro (c := (3 -rdRWNotIn {aa,bb,c})) refers 2 -ndRWNotIn {aa,bb,c} & not Stop SCM+FSA refers 2 -ndRWNotIn {aa,bb,c} ) by A7, Th2, Th3, SCMFSA8C:51;

per cases ( 0 = n or 0 < n ) ;

suppose A49: 0 = n ; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (intloc 0) = 1 & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )

thus ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (intloc 0) = 1 & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb ) :: thesis: verum

proof

thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (intloc 0) = 1 by A23, A14, A6, A30, A33, Th17; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )
A50: (Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)) . f = ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . 0) . f by A49, SCMFSA_M:37
.= s . f by A20, Th13 ;
A51: (Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)) . (3 -rdRWNotIn {aa,bb,c}) = ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . 0) . (3 -rdRWNotIn {aa,bb,c}) by A49, SCMFSA_M:37
.= s . aa by A14, Th9 ;
A52: (Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)) . bb = ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . 0) . bb by A5, A34, A49, SCMFSA_M:9, SCMFSA_M:37
.= (Exec ((c := aa),(Initialized s))) . bb by A11, Th11 ;
A53: (Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)) . aa = ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . 0) . aa by A4, A34, A49, SCMFSA_M:9, SCMFSA_M:37
.= (Exec ((c := aa),(Initialized s))) . aa by A17, Th10 ;
thus ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb ) :: thesis: verum

proof

per cases ( (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (2 -ndRWNotIn {aa,bb,c}) <= (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (1 -stRWNotIn {aa,bb,c}) or (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (2 -ndRWNotIn {aa,bb,c}) > (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (1 -stRWNotIn {aa,bb,c}) ) ;

suppose A54: (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (2 -ndRWNotIn {aa,bb,c}) <= (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (1 -stRWNotIn {aa,bb,c}) ; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )

hence ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = ((IExec ((Stop SCM+FSA),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . (3 -rdRWNotIn {aa,bb,c})) + 1 by A7, A48, A41, SCMFSA8B:40
.= (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) by A14, A44, A47, A49, A51, SCMFSA_M:2 ;
:: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (IExec ((Stop SCM+FSA),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . f by A48, A38, A54, SCMFSA8B:40
.= (Exec ((c := aa),(Initialized s))) . f by A20, A44, A42, A50, SCMFSA_M:2 ; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (IExec ((Stop SCM+FSA),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . aa by A19, A48, A40, A54, SCMFSA8B:40
.= (Exec ((c := aa),(Initialized s))) . aa by A44, A46, A53, SCMFSA_M:2 ; :: thesis: ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (IExec ((Stop SCM+FSA),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . bb by A13, A48, A39, A54, SCMFSA8B:40
.= (Exec ((c := aa),(Initialized s))) . bb by A44, A45, A52, SCMFSA_M:2 ; :: thesis: verum

end;

suppose A55: (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (2 -ndRWNotIn {aa,bb,c}) > (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (1 -stRWNotIn {aa,bb,c}) ; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )

A56: (IExec ((Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . (3 -rdRWNotIn {aa,bb,c}) = (Exec ((c := (3 -rdRWNotIn {aa,bb,c})),(Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))))) . (3 -rdRWNotIn {aa,bb,c}) by SCMFSA6C:5
.= (Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))) . (3 -rdRWNotIn {aa,bb,c}) by A22, SCMFSA_2:63 ;
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = ((Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))) . (3 -rdRWNotIn {aa,bb,c})) + 1 by A56, A7, A48, A41, A55, SCMFSA8B:40
.= (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) by A14, A47, A49, A51, SCMFSA_M:37 ; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (IExec ((Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . f by A48, A38, A55, SCMFSA8B:40
.= (Exec ((c := (3 -rdRWNotIn {aa,bb,c})),(Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))))) . f by SCMFSA6C:5
.= (Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))) . f by SCMFSA_2:63
.= (Exec ((c := aa),(Initialized s))) . f by A20, A42, A50, SCMFSA_M:37 ; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (IExec ((Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . aa by A19, A48, A40, A55, SCMFSA8B:40
.= (Exec ((c := (3 -rdRWNotIn {aa,bb,c})),(Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))))) . aa by SCMFSA6C:5
.= (Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))) . aa by A1, SCMFSA_2:63
.= (Exec ((c := aa),(Initialized s))) . aa by A4, A43, A46, A53, SCMFSA_M:9, SCMFSA_M:37 ; :: thesis: ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (IExec ((Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . bb by A13, A48, A39, A55, SCMFSA8B:40
.= (Exec ((c := (3 -rdRWNotIn {aa,bb,c})),(Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))))) . bb by SCMFSA6C:5
.= (Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))) . bb by A2, SCMFSA_2:63
.= (Exec ((c := aa),(Initialized s))) . bb by A5, A43, A45, A52, SCMFSA_M:9, SCMFSA_M:37 ; :: thesis: verum

end;

end;

end;

end;

end;

suppose A57: 0 < n ; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (intloc 0) = 1 & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )

thus ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (intloc 0) = 1 & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb ) :: thesis: verum

proof

thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (intloc 0) = 1 by A23, A14, A6, A30, A33, Th17; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )
A58: (Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)) . (3 -rdRWNotIn {aa,bb,c}) = ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n) . (3 -rdRWNotIn {aa,bb,c}) by SCMFSA_M:37;
A59: (Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)) . aa = (Exec ((c := aa),(Initialized s))) . aa by A4, A32, A33, A57, NAT_1:13, SCMFSA_M:9, SCMFSA_M:37;
A60: (Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)) . bb = (Exec ((c := aa),(Initialized s))) . bb by A5, A32, A33, A57, NAT_1:13, SCMFSA_M:9, SCMFSA_M:37;
A61: (Initialized ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)) . f = s . f by A20, A32, A33, A57, NAT_1:13, SCMFSA_M:37;
thus ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb ) :: thesis: verum

proof

per cases ( (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (2 -ndRWNotIn {aa,bb,c}) <= (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (1 -stRWNotIn {aa,bb,c}) or (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (2 -ndRWNotIn {aa,bb,c}) > (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (1 -stRWNotIn {aa,bb,c}) ) ;

suppose A62: (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (2 -ndRWNotIn {aa,bb,c}) <= (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (1 -stRWNotIn {aa,bb,c}) ; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )

hence ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = ((IExec ((Stop SCM+FSA),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . (3 -rdRWNotIn {aa,bb,c})) + 1 by A7, A48, A41, SCMFSA8B:40
.= ((IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (3 -rdRWNotIn {aa,bb,c})) + 1 by A44, SCMFSA_M:2
.= (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) by A34, A47, A58 ;
:: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (IExec ((Stop SCM+FSA),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . f by A48, A38, A62, SCMFSA8B:40
.= (Exec ((c := aa),(Initialized s))) . f by A20, A44, A42, A61, SCMFSA_M:2 ; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (IExec ((Stop SCM+FSA),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . aa by A19, A48, A40, A62, SCMFSA8B:40
.= (Exec ((c := aa),(Initialized s))) . aa by A44, A46, A59, SCMFSA_M:2 ; :: thesis: ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (IExec ((Stop SCM+FSA),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . bb by A13, A48, A39, A62, SCMFSA8B:40
.= (Exec ((c := aa),(Initialized s))) . bb by A44, A45, A60, SCMFSA_M:2 ; :: thesis: verum

end;

suppose A63: (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (2 -ndRWNotIn {aa,bb,c}) > (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (1 -stRWNotIn {aa,bb,c}) ; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )

A64: (IExec ((Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . (3 -rdRWNotIn {aa,bb,c}) = (Exec ((c := (3 -rdRWNotIn {aa,bb,c})),(Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))))) . (3 -rdRWNotIn {aa,bb,c}) by SCMFSA6C:5
.= (Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))) . (3 -rdRWNotIn {aa,bb,c}) by A22, SCMFSA_2:63
.= (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))) . (3 -rdRWNotIn {aa,bb,c}) by SCMFSA_M:37 ;
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . (3 -rdRWNotIn {aa,bb,c}) = ((IExec ((Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . (3 -rdRWNotIn {aa,bb,c})) + 1 by A7, A48, A41, A63, SCMFSA8B:40
.= (n + 1) + ((Exec ((c := aa),(Initialized s))) . aa) by A34, A47, A58, A64 ; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (Exec ((c := aa),(Initialized s))) . f & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . f = (IExec ((Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . f by A48, A38, A63, SCMFSA8B:40
.= (Exec ((c := (3 -rdRWNotIn {aa,bb,c})),(Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))))) . f by SCMFSA6C:5
.= (Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))) . f by SCMFSA_2:63
.= (Exec ((c := aa),(Initialized s))) . f by A20, A42, A61, SCMFSA_M:37 ; :: thesis: ( ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (Exec ((c := aa),(Initialized s))) . aa & ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb )
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . aa = (IExec ((Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . aa by A19, A48, A40, A63, SCMFSA8B:40
.= (Exec ((c := (3 -rdRWNotIn {aa,bb,c})),(Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))))) . aa by SCMFSA6C:5
.= (Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))) . aa by A1, SCMFSA_2:63
.= (Exec ((c := aa),(Initialized s))) . aa by A4, A43, A46, A59, SCMFSA_M:9, SCMFSA_M:37 ; :: thesis: ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (Exec ((c := aa),(Initialized s))) . bb
thus ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . (n + 1)) . bb = (IExec ((Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),(IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n))))) . bb by A13, A48, A39, A63, SCMFSA8B:40
.= (Exec ((c := (3 -rdRWNotIn {aa,bb,c})),(Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))))) . bb by SCMFSA6C:5
.= (Initialized (IExec ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))),(p +* (while>0 ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),((((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))) ";" (AddTo ((3 -rdRWNotIn {aa,bb,c}),(intloc 0)))) ";" (SubFrom ((1 -stRWNotIn ({(3 -rdRWNotIn {aa,bb,c}),aa,bb} \/ (UsedILoc ((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA))))))),(intloc 0))))))),((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . n)))) . bb by A2, SCMFSA_2:63
.= (Exec ((c := aa),(Initialized s))) . bb by A5, A43, A45, A60, SCMFSA_M:9, SCMFSA_M:37 ; :: thesis: verum

end;

end;

end;

end;

end;

end;

end;

A65: S₁[ 0 ] ;
A66: for n being Nat holds S₁[n] from NAT_1:sch 2(A65, A31);
A67: DataPart (IExec ((for-up ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))))),p,(Exec ((c := aa),(Initialized s))))) = DataPart ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . k) by A23, A14, A6, Th23;
thus (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . f = (IExec ((for-up ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))))),p,(Exec ((c := aa),(Initialized s))))) . f by A24, SFMASTR1:15
.= ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . k) . f by A67, SCMFSA_M:2
.= s . f by A20, A29, A66 ; :: thesis: ( (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . aa = s . aa & (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . bb = s . bb )
thus (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . aa = (IExec ((for-up ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))))),p,(Exec ((c := aa),(Initialized s))))) . aa by A24, SFMASTR1:14
.= ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . k) . aa by A67, SCMFSA_M:2
.= s . aa by A14, A29, A66 ; :: thesis: (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . bb = s . bb
thus (IExec ((FinSeqMin (f,aa,bb,c)),p,s)) . bb = (IExec ((for-up ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))))),p,(Exec ((c := aa),(Initialized s))))) . bb by A24, SFMASTR1:14
.= ((StepForUp ((3 -rdRWNotIn {aa,bb,c}),aa,bb,((((1 -stRWNotIn {aa,bb,c}) := (f,(3 -rdRWNotIn {aa,bb,c}))) ";" ((2 -ndRWNotIn {aa,bb,c}) := (f,c))) ";" (if>0 ((2 -ndRWNotIn {aa,bb,c}),(1 -stRWNotIn {aa,bb,c}),(Macro (c := (3 -rdRWNotIn {aa,bb,c}))),(Stop SCM+FSA)))),p,(Exec ((c := aa),(Initialized s))))) . k) . bb by A67, SCMFSA_M:2
.= s . bb by A6, A29, A66 ; :: thesis: verum

end;

end;