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
  NeutralProcess(N) concur R = R
proof
  thus NeutralProcess(N) concur R c= R
  proof
    let x be object;
    assume x in NeutralProcess(N) concur R;
    then consider C such that
A1: x = C and
A2: ex q1,q2 being FinSubsequence st C = q1 \/ q2 & q1 misses q2 & Seq
    q1 in {<*>N} & Seq q2 in R;
    consider q1,q2 being FinSubsequence such that
A3: C = q1 \/ q2
    and q1 misses q2 and
A4: Seq q1 in {<*>N} and
A5: Seq q2 in R by A2;
    Seq q1 = {} by A4,TARSKI:def 1;
    then q1 = {} by FINSEQ_1:97;
    hence thesis by A1,A3,A5,FINSEQ_3:116;
  end;
  let x be object;
  assume
A6: x in R;
  then reconsider C = x as firing-sequence of N;
  reconsider q1 = <*>N, q2 = C as FinSubsequence;
A7: Seq q2 = C by FINSEQ_3:116;
A8: {} \/ q2 = C;
A9: Seq q1 = q1 by FINSEQ_3:116;
A10: q1 in {<*>N} by TARSKI:def 1;
  q1 misses q2;
  hence thesis by A6,A7,A8,A9,A10;
end;
