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 Th20:
  for TS being transition-system over F holds x1, x2 ==>. y1, y2,
TS implies x1 in TS & y1 in TS & x2 in E^omega & y2 in E^omega & x1 in dom dom
  (the Tran of TS) & y1 in rng (the Tran of TS)
by Th15;
