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;

theorem
  {C1,C2} before {C} = {C1^C, C2^C}
proof
  thus
  {C1,C2} before {C} = ({C1} \/ {C2}) before {C} by ENUMSET1:1
    .= ({C1} before {C}) \/ ({C2} before {C}) by Th29
    .= {C1^C} \/ ({C2} before {C}) by Th31
    .= {C1^C} \/ {C2^C} by Th31
    .= {C1^C, C2^C} by ENUMSET1:1;
end;
