theorem
  R before NeutralProcess(N) = R
proof
  thus R before NeutralProcess N c= R
  proof
    let x be object;
    assume x in R before NeutralProcess N;
    then consider C1,C such that
A1: x = C1^C and
A2: C1 in R and
A3: C in NeutralProcess(N);
    C = <*>N by A3,TARSKI:def 1;
    hence thesis by A1,A2,FINSEQ_1:34;
  end;
  let x be object;
  assume
A4: x in R;
  then reconsider C = x as Element of N*;
A5: <*>N in NeutralProcess(N) by TARSKI:def 1;
  x = C^(<*>N) by FINSEQ_1:34;
  hence thesis by A4,A5;
end;
