theorem
  for s1,s2 be State of S holds
  DataPart s1 = DataPart s2 implies
    Initialize s1 =  Initialize s2
proof
  let s1,s2 be State of S;
  assume
A1: DataPart s1 = DataPart s2;
  set S1 = Initialize s1, S2 = Initialize s2;
A2: IC S1 =  0 & IC S2 =  0 by Th47;
  DataPart S1 = DataPart s1 by Th45
    .= DataPart S2 by A1,Th45;
  hence thesis by A2,Th78;
end;
