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 Th33:
  x in ==>.-relation(TS) implies ex s, t, v, w st x = [[s, v], [t, w]]
proof
  assume
A1: x in ==>.-relation(TS);
  then consider y, z being object such that
A2: x = [y, z] by RELAT_1:def 1;
  ex s, v, t, w st y = [s, v] & z = [t, w] by A1,A2,Th31;
  hence thesis by A2;
end;
