reserve i,j,k,l for Nat,
  x,x1,x2,y1,y2 for set;
reserve P,p,x,y,x1,x2 for set,
  m1,m2,m3,m4,m for marking of P,
  i,j,j1,j2,k,k1,k2,l,l1 for Nat;
reserve t,t1,t2 for transition of P;
reserve N for Petri_net of P;
reserve e, e1,e2 for Element of N;
reserve C,C1,C2,C3,fs,fs1,fs2 for firing-sequence of N;
reserve R, R1, R2, R3, P1, P2 for process of N;
reserve q,q1,q2,q3,q4 for FinSubsequence,
        p1,p2 for FinSequence;

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;
