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;
reserve TS for non empty transition-system over F;
reserve s, s9, s1, s2, t, t1, t2 for Element of TS;
reserve S for Subset of TS;

theorem
  TS is deterministic implies ==>.-relation(TS) is Function-like
proof
  assume TS is deterministic;
  then
  for x, y, z being object
st [x, y] in ==>.-relation(TS) & [x, z] in ==>.-relation(TS)
  holds y = z by Th44;
  hence thesis by FUNCT_1:def 1;
end;
