theorem Th45:
  for s being State of SCMPDS,I being Program of SCMPDS,a,b being
  Int_position, i being Integer,n be Nat st s.DataLoc(s.a,i) <= 0
  holds IExec(for-down(a,i,n,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,n be Nat;
  assume s.DataLoc(s.a,i) <= 0;
  then
A1: IExec(for-down(a,i,n,I),P,Initialize s) = s +* Start-At((card I+3),SCMPDS)
by Th43;
  not b in dom Start-At((card I+3),SCMPDS) by SCMPDS_4:18;
  hence thesis by A1,FUNCT_4:11;
end;
