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 a be Int_position,s1,s2 being State of SCMPDS st DataPart s1
  = DataPart s2 holds s1.a=s2.a
proof
  let 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;
  hence s1.a= (DataPart s1).a by FUNCT_1:49,SCMPDS_2:84
    .= s2.a by A1,A2,FUNCT_1:49,SCMPDS_2:84;
end;
