let P be Instruction-Sequence of SCMPDS; :: thesis: 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) + 2
let s be State of SCMPDS; :: thesis: 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) + 2
let I be halt-free parahalting shiftable Program of ; :: thesis: for a being Int_position
for k1 being Integer holds IC (IExec ((if<>0 (a,k1,I)),P,(Initialize s))) = (card I) + 2
let a be Int_position; :: thesis: for k1 being Integer holds IC (IExec ((if<>0 (a,k1,I)),P,(Initialize s))) = (card I) + 2
let k1 be Integer; :: thesis: IC (IExec ((if<>0 (a,k1,I)),P,(Initialize 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;

per cases ( s . (DataLoc ((s . a),k1)) <> 0 or s . (DataLoc ((s . a),k1)) = 0 ) ;

suppose s . (DataLoc ((s . a),k1)) <> 0 ; :: thesis: IC (IExec ((if<>0 (a,k1,I)),P,(Initialize s))) = (card I) + 2

then IExec ((if<>0 (a,k1,I)),P,(Initialize s)) = (IExec (I,P,(Initialize s))) +* (Start-At (((card I) + 2),SCMPDS)) by A1, Th51;
hence IC (IExec ((if<>0 (a,k1,I)),P,(Initialize s))) = (card I) + 2 by FUNCT_4:113; :: thesis: verum

end;

suppose s . (DataLoc ((s . a),k1)) = 0 ; :: thesis: IC (IExec ((if<>0 (a,k1,I)),P,(Initialize s))) = (card I) + 2

then IExec ((if<>0 (a,k1,I)),P,(Initialize s)) = s +* (Start-At (((card I) + 2),SCMPDS)) by Th52;
hence IC (IExec ((if<>0 (a,k1,I)),P,(Initialize s))) = (card I) + 2 by FUNCT_4:113; :: thesis: verum

end;

end;