reserve x, y, X for set;
reserve E for non empty set;
reserve e for Element of E;
reserve u, u1, v, v1, v2, w, w9, w1, w2 for Element of E^omega;
reserve F for Subset of E^omega;
reserve i, k, l for Nat;
reserve TS for non empty transition-system over F;
reserve S, T for Subset of TS;

theorem Th6:
  for p, q being XFinSequence st <%x%>^p = <%y%>^q holds x = y & p = q
proof
  let p, q be XFinSequence such that
A1: <%x%>^p = <%y%>^q;
  (<%x%>^p).0 = x by AFINSQ_1:35;
  then x = y by A1,AFINSQ_1:35;
  hence thesis by A1,AFINSQ_1:28;
end;
