
theorem Th11:
  for PTN being Petri_net, M0 being Boolean_marking of PTN, t
  being transition of PTN holds Firing(t,M0) = Firing(<*t*>,M0)
proof
  let PTN be Petri_net, M0 be Boolean_marking of PTN, t be transition of PTN;
  set M = <*Firing(<*t*>/.1,M0)*>;
A1: len <*t*> = 1 & <*t*>/.1 = t by FINSEQ_1:39,FINSEQ_4:16;
A2: M/.1 = Firing(<*t*>/.1,M0) by FINSEQ_4:16;
A3: now
A4: len <*t*> = 0 + 1 by FINSEQ_1:39;
    let i be Nat;
    assume i < len <*t*> & i > 0;
    hence M/.(i+1) = Firing(<*t*>/.(i+1),M/.i) by A4,NAT_1:13;
  end;
  len <*t*> = 1 by FINSEQ_1:39
    .= len M by FINSEQ_1:39;
  hence thesis by A1,A2,A3,Def5;
end;
