reserve x, y, X for set;
reserve E for non empty set;
reserve e for Element of E;
reserve u, u1, v, v1, v2, w, w9, w1, w2 for Element of E^omega;
reserve F for Subset of E^omega;
reserve i, k, l for Nat;
reserve TS for non empty transition-system over F;
reserve S, T for Subset of TS;
reserve SA for non empty semiautomaton over F;
reserve A for non empty automaton over F;
reserve p, q for Element of A;

theorem Th17:
  for Q being Subset of A holds w in right-Lang(Q) iff w-succ_of (
  Q, A) meets (the FinalS of A)
proof
  let Q be Subset of A;
  thus w in right-Lang(Q) implies w-succ_of (Q, A) meets (the FinalS of A)
  proof
    assume w in right-Lang(Q);
    then ex w9 st w = w9 & w9-succ_of (Q, A) meets (the FinalS of A);
    hence thesis;
  end;
  thus thesis;
end;
