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
  R1 c= P1 & R2 c= P2 implies R1 before R2 c= P1 before P2
proof
  assume that
A1: R1 c= P1 and
A2: R2 c= P2;
  let x be object;
  assume x in R1 before R2;
  then ex C1,C2 st ( x = C1^C2)&( C1 in R1)&( C2 in R2);
  hence thesis by A1,A2;
end;
