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 Th8:
  for R being Relation holds <*x, y*> is RedSequence of R implies [x, y] in R
proof
  let R be Relation;
  set P = <*x, y*>;
A1: P.1 = x & P.2 = y;
  len P = 2 by FINSEQ_1:44;
  then 1 in dom P & 1 + 1 in dom P by FINSEQ_3:25;
  hence thesis by A1,REWRITE1:def 2;
end;
