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 Th59:
  for P being RedSequence of ==>.-relation(TS) st P.1 = [x, v] & P
  .len P = [y, w] holds len v >= len w
proof
  let P be RedSequence of ==>.-relation(TS);
  assume P.1 = [x, v] & P.len P = [y, w];
  then ex u st v = u^w by Th53;
  hence thesis by Th9;
end;
