theorem
  for s being State of SCMPDS,I being Program of SCMPDS,a,b being
Int_position, k1 being Integer st s.DataLoc(s.a,k1) >= 0
 holds IExec(if<0(a,k1,I),P,Initialize s).b = s.b
proof
  let s be State of SCMPDS,I be Program of SCMPDS,a,b be Int_position, k1 be
  Integer;
  assume
  s.DataLoc(s.a,k1) >= 0;
  then
A1: IExec(if<0(a,k1,I),P,Initialize s) = s +* Start-At((card I+1),SCMPDS)
      by Th102;
  not b in dom Start-At((card I+1),SCMPDS) by SCMPDS_4:18;
  hence thesis by A1,FUNCT_4:11;
end;
