let P be Instruction-Sequence of SCMPDS; for s being 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,(Initialize s))) = (card I) + 1
let s be 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,(Initialize s))) = (card I) + 1
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,(Initialize s))) = (card I) + 1
let a be Int_position; for k1 being Integer holds IC (IExec ((if<0 (a,k1,I)),P,(Initialize s))) = (card I) + 1
let k1 be Integer; IC (IExec ((if<0 (a,k1,I)),P,(Initialize s))) = (card I) + 1
set IF = if<0 (a,k1,I);
A1:
( I is_closed_on s,P & I is_halting_on s,P )
by Th11, Th12;
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,(Initialize s))) = (card I) + 1then
IExec (
(if<0 (a,k1,I)),
P,
(Initialize s))
= (IExec (I,P,(Initialize s))) +* (Start-At (((card I) + 1),SCMPDS))
by A1, Th101;
hence
IC (IExec ((if<0 (a,k1,I)),P,(Initialize s))) = (card I) + 1
by FUNCT_4:113;
verum end; end;