let P be Instruction-Sequence of SCMPDS; for s being 0 -started State of SCMPDS
for I being halt-free parahalting shiftable Program of
for a being Int_position
for k1 being Integer holds IC (IExec ((if>=0 (a,k1,I)),P,s)) = (card I) + 2
let s be 0 -started State of SCMPDS; for I being halt-free parahalting shiftable Program of
for a being Int_position
for k1 being Integer holds IC (IExec ((if>=0 (a,k1,I)),P,s)) = (card I) + 2
let I be halt-free parahalting shiftable Program of ; for a being Int_position
for k1 being Integer holds IC (IExec ((if>=0 (a,k1,I)),P,s)) = (card I) + 2
let a be Int_position; for k1 being Integer holds IC (IExec ((if>=0 (a,k1,I)),P,s)) = (card I) + 2
let k1 be Integer; IC (IExec ((if>=0 (a,k1,I)),P,s)) = (card I) + 2
set IF = if>=0 (a,k1,I);
A1:
( I is_closed_on s,P & I is_halting_on s,P )
by Th11, Th12;
A2:
Initialize s = s
by MEMSTR_0:44;
per cases
( s . (DataLoc ((s . a),k1)) >= 0 or s . (DataLoc ((s . a),k1)) < 0 )
;
suppose
s . (DataLoc ((s . a),k1)) >= 0
;
IC (IExec ((if>=0 (a,k1,I)),P,s)) = (card I) + 2then
IExec (
(if>=0 (a,k1,I)),
P,
s)
= (IExec (I,P,s)) +* (Start-At (((card I) + 2),SCMPDS))
by A1, Th111, A2;
hence
IC (IExec ((if>=0 (a,k1,I)),P,s)) = (card I) + 2
by FUNCT_4:113;
verum end; suppose
s . (DataLoc ((s . a),k1)) < 0
;
IC (IExec ((if>=0 (a,k1,I)),P,s)) = (card I) + 2then
IExec (
(if>=0 (a,k1,I)),
P,
s)
= s +* (Start-At (((card I) + 2),SCMPDS))
by Th112, A2;
hence
IC (IExec ((if>=0 (a,k1,I)),P,s)) = (card I) + 2
by FUNCT_4:113;
verum end; end;