set WHL = while>0 (F₅(),F₆(),F₄());
set pWHL = stop (while>0 (F₅(),F₆(),F₄()));
set s1 = Initialize F₂();
set ps = ProgramPart F₂();
set P1 = F₃() +* (stop (while>0 (F₅(),F₆(),F₄())));
set sI = Initialize F₂();
set PI = F₃() +* (stop F₄());
set m1 = (LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 2;
set s2 = Initialize (IExec (F₄(),F₃(),F₂()));
set P2 = F₃() +* (stop (while>0 (F₅(),F₆(),F₄())));
set m2 = LifeSpan ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize (IExec (F₄(),F₃(),F₂()))));
A9: P₁[ Dstate F₂()] by A4;
A10: stop F₄() c= F₃() +* (stop F₄()) by FUNCT_4:26;
B10: Start-At (0,SCMPDS) c= Initialize F₂() by FUNCT_4:26;
F₄() is_closed_on F₂(),F₃() by A2, A4, A5;
then A11: F₄() is_closed_on Initialize F₂(),F₃() +* (stop F₄()) by SCMPDS_6:38;
F₄() is_halting_on F₂(),F₃() by A2, A4, A5;
then A12: F₃() +* (stop F₄()) halts_on Initialize F₂() by SCMPDS_6:def 3;
F₃() +* (stop F₄()) = (F₃() +* (stop F₄())) +* (stop F₄()) by A10, FUNCT_4:104;
then (F₃() +* (stop F₄())) +* (stop F₄()) halts_on Initialize (Initialize F₂()) by A12;
then A14: F₄() is_halting_on Initialize F₂(),F₃() +* (stop F₄()) by SCMPDS_6:def 3;
set Es = IExec (F₄(),F₃(),F₂());
set bj = DataLoc (((IExec (F₄(),F₃(),F₂())) . F₅()),F₆());
set EP = F₃();
deffunc H₁( State of SCMPDS) -> Element of NAT = F₁($1);
A15: for t being State of SCMPDS
for Q being the Instructions of SCMPDS -valued ManySortedSet of NAT st P₁[ Dstate t] & t . F₅() = F₂() . F₅() & t . (DataLoc ((F₂() . F₅()),F₆())) > 0 holds
( (IExec (F₄(),Q,t)) . F₅() = t . F₅() & F₄() is_closed_on t,Q & F₄() is_halting_on t,Q & H₁( Dstate (IExec (F₄(),Q,t))) < H₁( Dstate t) & P₁[ Dstate (IExec (F₄(),Q,t))] ) by A5;
A16: for t being State of SCMPDS st P₁[ Dstate t] & H₁( Dstate t) = 0 holds
t . (DataLoc ((F₂() . F₅()),F₆())) <= 0 by A3;
( ( H₁(F₂()) = H₁(F₂()) or P₁[F₂()] ) & while>0 (F₅(),F₆(),F₄()) is_closed_on F₂(),F₃() & while>0 (F₅(),F₆(),F₄()) is_halting_on F₂(),F₃() ) from SCMPDS_8:sch 3(A16, A9, A15);
then A17: F₃() +* (stop (while>0 (F₅(),F₆(),F₄()))) halts_on Initialize F₂() by SCMPDS_6:def 3;
deffunc H₂( State of SCMPDS) -> Element of NAT = F₁($1);
A18: (IExec (F₄(),F₃(),F₂())) . F₅() = F₂() . F₅() by A2, A4, A5;
then A19: for t being State of SCMPDS st P₁[ Dstate t] & H₂( Dstate t) = 0 holds
t . (DataLoc (((IExec (F₄(),F₃(),F₂())) . F₅()),F₆())) <= 0 by A3;
A20: for t being State of SCMPDS
for Q being the Instructions of SCMPDS -valued ManySortedSet of NAT st P₁[ Dstate t] & t . F₅() = (IExec (F₄(),F₃(),F₂())) . F₅() & t . (DataLoc (((IExec (F₄(),F₃(),F₂())) . F₅()),F₆())) > 0 holds
( (IExec (F₄(),Q,t)) . F₅() = t . F₅() & F₄() is_closed_on t,Q & F₄() is_halting_on t,Q & H₂( Dstate (IExec (F₄(),Q,t))) < H₂( Dstate t) & P₁[ Dstate (IExec (F₄(),Q,t))] ) by A5, A18;
A21: P₁[ Dstate (IExec (F₄(),F₃(),F₂()))] by A2, A4, A5;
( ( H₂( IExec (F₄(),F₃(),F₂())) = H₂( IExec (F₄(),F₃(),F₂())) or P₁[ IExec (F₄(),F₃(),F₂())] ) & while>0 (F₅(),F₆(),F₄()) is_closed_on IExec (F₄(),F₃(),F₂()),F₃() & while>0 (F₅(),F₆(),F₄()) is_halting_on IExec (F₄(),F₃(),F₂()),F₃() ) from SCMPDS_8:sch 3(A19, A21, A20);
then A22: F₃() +* (stop (while>0 (F₅(),F₆(),F₄()))) halts_on Initialize (IExec (F₄(),F₃(),F₂())) by SCMPDS_6:def 3;
set s4 = Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),1);
set P4 = F₃() +* (stop (while>0 (F₅(),F₆(),F₄())));
set i1 = (F₅(),F₆()) <=0_goto ((card F₄()) + 2);
set i2 = goto (- ((card F₄()) + 1));
set b = DataLoc ((F₂() . F₅()),F₆());
A23: while>0 (F₅(),F₆(),F₄()) = ((F₅(),F₆()) <=0_goto ((card F₄()) + 2)) ';' (F₄() ';' (goto (- ((card F₄()) + 1)))) by SCMPDS_4:51;
set mI = LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()));
set s5 = Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),1)),(LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))));
set P5 = F₃() +* (stop (while>0 (F₅(),F₆(),F₄())));
set l1 = (card F₄()) + 1;
A24: IC (Initialize F₂()) = 0 by COMPOS_1:def 16;
A25: Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),(0 + 1)) = Following ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),0))) by EXTPRO_1:4
.= Following ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂())) by EXTPRO_1:3
.= Exec (((F₅(),F₆()) <=0_goto ((card F₄()) + 2)),(Initialize F₂())) by A23, SCMPDS_6:22 ;

now

let a be Int_position ; :: thesis: (Initialize F₂()) . a = (Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),1)) . a
thus (Initialize F₂()) . a = (Initialize F₂()) . a
.= (Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),1)) . a by A25, SCMPDS_2:68 ; :: thesis: verum

end;

then A27: DataPart (Initialize F₂()) = DataPart (Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),1)) by SCMPDS_4:23;
set m3 = (LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 1;
set s6 = Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 1));
set P6 = F₃() +* (stop (while>0 (F₅(),F₆(),F₄())));
(card F₄()) + 1 < (card F₄()) + 2 by XREAL_1:8;
then A28: (card F₄()) + 1 in dom (while>0 (F₅(),F₆(),F₄())) by Th18;
thus ( F₁(F₂()) = F₁(F₂()) or P₁[F₂()] ) ; :: thesis: IExec ((while>0 (F₅(),F₆(),F₄())),F₃(),F₂()) = IExec ((while>0 (F₅(),F₆(),F₄())),F₃(),(IExec (F₄(),F₃(),F₂())))
set m0 = LifeSpan ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()));
A29: dom (ProgramPart F₂()) = (dom F₂()) /\ NAT by RELAT_1:90
.= (({(IC )} \/ SCM-Data-Loc) \/ NAT) /\ NAT by SCMPDS_4:19
.= NAT by XBOOLE_1:21 ;
A30: (IExec (F₄(),F₃(),F₂())) | NAT = ((Result ((F₃() +* (stop F₄())),(Initialize F₂()))) +* (ProgramPart F₂())) | NAT by SCMPDS_4:def 8
.= ProgramPart F₂() by A29, FUNCT_4:24 ;
set s7 = Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),(((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 1) + 1));
A31: IExec (F₄(),F₃(),F₂()) = (Result ((F₃() +* (stop F₄())),(Initialize F₂()))) +* (F₂() | NAT) by SCMPDS_4:def 8;
A32: dom (ProgramPart F₂()) = NAT by COMPOS_1:34;
XX: while>0 (F₅(),F₆(),F₄()) c= stop (while>0 (F₅(),F₆(),F₄())) by AFINSQ_1:78;
stop (while>0 (F₅(),F₆(),F₄())) c= F₃() +* (stop (while>0 (F₅(),F₆(),F₄()))) by FUNCT_4:26;
then A33: while>0 (F₅(),F₆(),F₄()) c= F₃() +* (stop (while>0 (F₅(),F₆(),F₄()))) by XBOOLE_1:1, XX;
Shift (F₄(),1) c= while>0 (F₅(),F₆(),F₄()) by Lm4;
then Shift (F₄(),1) c= F₃() +* (stop (while>0 (F₅(),F₆(),F₄()))) by A33, XBOOLE_1:1;
then A34: Shift (F₄(),1) c= F₃() +* (stop (while>0 (F₅(),F₆(),F₄()))) ;
TT: not DataLoc ((F₂() . F₅()),F₆()) in dom (Start-At (0,SCMPDS)) by SCMPDS_4:59;
not F₅() in dom (Start-At (0,SCMPDS)) by SCMPDS_4:59;
then (Initialize F₂()) . (DataLoc (((Initialize F₂()) . F₅()),F₆())) = (Initialize F₂()) . (DataLoc ((F₂() . F₅()),F₆())) by FUNCT_4:12
.= F₂() . (DataLoc ((F₂() . F₅()),F₆())) by TT, FUNCT_4:12 ;
then A35: IC (Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),1)) = succ (IC (Initialize F₂())) by A2, A25, SCMPDS_2:68
.= 0 + 1 by A24 ;
then A36: IC (Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),1)),(LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))))) = (card F₄()) + 1 by A10, B10, A14, A11, A27, A34, SCMPDS_7:36;
A37: (F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))) /. (IC (Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 1)))) = (F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))) . (IC (Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 1)))) by PBOOLE:158;
A38: Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 1)) = Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),1)),(LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂())))) by EXTPRO_1:5;
then A39: CurInstr ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 1)))) = (F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))) . ((card F₄()) + 1) by A10, B10, A14, A11, A35, A27, A34, A37, SCMPDS_7:36
.= (F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))) . ((card F₄()) + 1)
.= (F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))) . ((card F₄()) + 1)
.= (while>0 (F₅(),F₆(),F₄())) . ((card F₄()) + 1) by A28, A33, GRFUNC_1:8
.= goto (- ((card F₄()) + 1)) by Th19 ;
A41: Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),(((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 1) + 1)) = Following ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 1)))) by EXTPRO_1:4
.= Exec ((goto (- ((card F₄()) + 1))),(Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 1)))) by A39 ;
then IC (Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),(((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 1) + 1))) = ICplusConst ((Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 1))),(0 - ((card F₄()) + 1))) by SCMPDS_2:66
.= 0 by A36, A38, SCMPDS_7:1 ;
then A42: IC (Initialize (IExec (F₄(),F₃(),F₂()))) = IC (Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 2))) by COMPOS_1:def 16;
A43: DataPart (Comput ((F₃() +* (stop F₄())),(Initialize F₂()),(LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))))) = DataPart (Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),1)),(LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))))) by A10, B10, A14, A11, A35, A27, A34, SCMPDS_7:36;

now

let x be Int_position ; :: thesis: (Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),(((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 1) + 1))) . x = (Initialize (IExec (F₄(),F₃(),F₂()))) . x
A44: not x in dom (Start-At (0,SCMPDS)) by SCMPDS_4:59;
A45: not x in dom (F₂() | NAT) by A32, SCMPDS_2:53;
(Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),1)),(LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))))) . x = (Comput ((F₃() +* (stop F₄())),(Initialize F₂()),(LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))))) . x by A43, SCMPDS_4:23
.= (Result ((F₃() +* (stop F₄())),(Initialize F₂()))) . x by A12, EXTPRO_1:23
.= (IExec (F₄(),F₃(),F₂())) . x by A31, A45, FUNCT_4:12 ;
hence (Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),(((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 1) + 1))) . x = (IExec (F₄(),F₃(),F₂())) . x by A38, A41, SCMPDS_2:66
.= (Initialize (IExec (F₄(),F₃(),F₂()))) . x by A44, FUNCT_4:12 ;
:: thesis: verum

end;

then A46: DataPart (Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),(((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 1) + 1))) = DataPart (Initialize (IExec (F₄(),F₃(),F₂()))) by SCMPDS_4:23;
ProgramPart (Initialize (IExec (F₄(),F₃(),F₂()))) = ProgramPart (IExec (F₄(),F₃(),F₂())) by COMPOS_1:206
.= ProgramPart ((Result ((F₃() +* (stop F₄())),(Initialize F₂()))) +* (ProgramPart F₂())) by SCMPDS_4:def 8
.= ProgramPart ((Result ((F₃() +* (stop F₄())),(Initialize F₂()))) +* (ProgramPart F₂()))
.= ProgramPart F₂() by A29, FUNCT_4:24
.= ProgramPart (Initialize F₂()) by COMPOS_1:206
.= ProgramPart (Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 2))) by AMI_1:123 ;
then A48: Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 2)) = Initialize (IExec (F₄(),F₃(),F₂())) by A46, A42, SCMPDS_7:7;
then CurInstr ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 2)))) = (F₅(),F₆()) <=0_goto ((card F₄()) + 2) by A23, SCMPDS_6:22;
then LifeSpan ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂())) > (LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 2 by A17, SCMPDS_6:2, SCMPDS_6:30;
then consider nn being Nat such that
A49: LifeSpan ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂())) = ((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 2) + nn by NAT_1:10;
reconsider nn = nn as Element of NAT by ORDINAL1:def 13;
Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),(((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 2) + (LifeSpan ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize (IExec (F₄(),F₃(),F₂()))))))) = Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize (IExec (F₄(),F₃(),F₂()))),(LifeSpan ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize (IExec (F₄(),F₃(),F₂())))))) by A48, EXTPRO_1:5;
then CurInstr ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),(((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 2) + (LifeSpan ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize (IExec (F₄(),F₃(),F₂()))))))))) = halt SCMPDS by A22, EXTPRO_1:def 14;
then ((LifeSpan ((F₃() +* (stop F₄())),(Initialize F₂()))) + 2) + (LifeSpan ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize (IExec (F₄(),F₃(),F₂()))))) >= LifeSpan ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂())) by A17, EXTPRO_1:def 14;
then A51: LifeSpan ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize (IExec (F₄(),F₃(),F₂())))) >= nn by A49, XREAL_1:8;
A52: Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂()),(LifeSpan ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂())))) = Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize (IExec (F₄(),F₃(),F₂()))),nn) by A48, A49, EXTPRO_1:5;
then CurInstr ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize (IExec (F₄(),F₃(),F₂()))),nn))) = halt SCMPDS by A17, EXTPRO_1:def 14;
then nn >= LifeSpan ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize (IExec (F₄(),F₃(),F₂())))) by A22, EXTPRO_1:def 14;
then nn = LifeSpan ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize (IExec (F₄(),F₃(),F₂())))) by A51, XXREAL_0:1;
then Result ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize F₂())) = Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize (IExec (F₄(),F₃(),F₂()))),(LifeSpan ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize (IExec (F₄(),F₃(),F₂())))))) by A17, A52, EXTPRO_1:23;
hence IExec ((while>0 (F₅(),F₆(),F₄())),F₃(),F₂()) = (Comput ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize (IExec (F₄(),F₃(),F₂()))),(LifeSpan ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize (IExec (F₄(),F₃(),F₂()))))))) +* (ProgramPart F₂()) by SCMPDS_4:def 8
.= (Result ((F₃() +* (stop (while>0 (F₅(),F₆(),F₄())))),(Initialize (IExec (F₄(),F₃(),F₂()))))) +* ((IExec (F₄(),F₃(),F₂())) | NAT) by A22, A30, EXTPRO_1:23
.= IExec ((while>0 (F₅(),F₆(),F₄())),F₃(),(IExec (F₄(),F₃(),F₂()))) by SCMPDS_4:def 8 ;
:: thesis: verum