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
  {<*e1*>,<*e2*>} concur {<*e*>} = {<*e1,e*>, <*e2,e*>, <*e,e1*>, <*e,e2*>}
proof
  {<*e1*>,<*e2*>} = {<*e1*>} \/ {<*e2*>} by ENUMSET1:1;
  then
A1: {<*e1*>,<*e2*>} concur {<*e*>}
  = {<*e1*>} concur {<*e*>} \/ {<*e2*>} concur {<*e*>} by Th34;
A2: {<*e1*>} concur {<*e*>} = {<*e1,e*>,<*e,e1*>} by Th35;
  {<*e2*>} concur {<*e*>} = {<*e2,e*>,<*e,e2*>} by Th35;
  hence {<*e1*>,<*e2*>} concur {<*e*>}
  = {<*e1,e*>, <*e,e1*>, <*e2,e*>, <*e,e2*>} by A1,A2,ENUMSET1:5
    .= {<*e1,e*>, <*e2,e*>, <*e,e1*>, <*e,e2*>} by ENUMSET1:62;
end;
