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 R being Relation, P being RedSequence of R st len P > 1 holds
  ex Q being RedSequence of R st
  len Q + 1 = len P & for k st k in dom Q holds Q.k = P.(k + 1)
proof
  let R be Relation, P be RedSequence of R;
  assume len P > 1;
  then consider Q being RedSequence of R such that
A1: P = <*P.1*>^Q & len Q + 1 = len P by Th5;
  take Q;
  thus thesis by A1,FINSEQ_3:103;
end;
