reserve j, k, m, n for Nat,
  a,b for Int_position,
  k1,k2 for Integer;
reserve P,P1,P2 for Instruction-Sequence of SCMPDS;

theorem
  for k1 be Integer,a be Int_position,s1,s2 being State of SCMPDS
  st DataPart s1 = DataPart s2 holds s1.DataLoc(s1.a,k1)=s2.DataLoc(s2.a,k1)
proof
  let k1 be Integer,a be Int_position,s1,s2 be State of SCMPDS;
  assume
A1: DataPart s1 = DataPart s2;
A2: a in SCM-Data-Loc by AMI_2:def 16;
  then
A3: s1.a= (DataPart s1).a by FUNCT_1:49,SCMPDS_2:84
    .= s2.a by A1,A2,FUNCT_1:49,SCMPDS_2:84;
A4: DataLoc(s1.a,k1) in SCM-Data-Loc by AMI_2:def 16;
  hence s1.DataLoc(s1.a,k1)= (DataPart s1).DataLoc(s1.a,k1) by FUNCT_1:49
,SCMPDS_2:84
    .= s2.DataLoc(s2.a,k1) by A1,A4,A3,FUNCT_1:49,SCMPDS_2:84;
end;
