reserve m,n for Element of NAT,
  i,j for Instruction of SCMPDS,
  I for Program
  of SCMPDS,
  a for Int_position;
reserve Q,U,P for Instruction-Sequence of SCMPDS;

theorem Th15:
  for s being State of SCMPDS,I being Program of SCMPDS,a,b being
Int_position, i being Integer st s.DataLoc(s.a,i) = 0
 holds IExec(while<>0(a,i,I),P,Initialize s).b = s.b
proof
  let s be State of SCMPDS,I be Program of SCMPDS,a,b be Int_position, i be
  Integer;
  assume s.DataLoc(s.a,i) = 0;
  then
A1: IExec(while<>0(a,i,I),P,Initialize s) = s +* Start-At((card I+3),SCMPDS)
 by Th13;
  not b in dom Start-At((card I+3),SCMPDS) by SCMPDS_4:18;
  hence thesis by A1,FUNCT_4:11;
end;
