let P be Instruction-Sequence of SCMPDS; :: thesis: for s being State of SCMPDS
for I being halt-free parahalting shiftable Program of SCMPDS
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; :: thesis: for I being halt-free parahalting shiftable Program of SCMPDS
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 SCMPDS; :: thesis: 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 ; :: thesis: for k1 being Integer holds IC (IExec ((if<0 (a,k1,I)),P,(Initialize s))) = (card I) + 1
let k1 be Integer; :: thesis: 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 Th34, Th35;

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) + 1

then IExec ((if<0 (a,k1,I)),P,(Initialize s)) = (IExec (I,P,(Initialize s))) +* (Start-At (((card I) + 1),SCMPDS)) by A1, Th124;
hence IC (IExec ((if<0 (a,k1,I)),P,(Initialize s))) = (card I) + 1 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) + 1

then IExec ((if<0 (a,k1,I)),P,(Initialize s)) = s +* (Start-At (((card I) + 1),SCMPDS)) by Th125;
hence IC (IExec ((if<0 (a,k1,I)),P,(Initialize s))) = (card I) + 1 by FUNCT_4:113; :: thesis: verum

end;

end;