reserve x, x1, x2, y, y1, y2, z, z1, z2 for object, X, X1, X2 for set;
reserve E for non empty set;
reserve e for Element of E;
reserve u, u9, u1, u2, v, v1, v2, w, w1, w2 for Element of E^omega;
reserve F, F1, F2 for Subset of E^omega;
reserve i, k, l, n for Nat;

theorem
  for TS1 being transition-system over X1, TS2 being
transition-system over X2 st the Tran of TS1 = the Tran of TS2 holds x, y -->.
  z, TS1 implies x, y -->. z, TS2;
