reserve k,n for Nat,
  x,y,z,y1,y2 for object,X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for XFinSequence;
reserve D for set;
reserve i for Nat;
reserve m for Nat,
        D for non empty set;
reserve l for Nat;
reserve M for Nat;
reserve m,n for Nat;
reserve x1,x2,x3,x4 for object;
reserve e,u for object;

theorem Th14:
  for D being set, p being XFinSequence of D, n being Nat
  holds n in dom p iff n+1 in dom XFS2FS p
proof
  let D be set, p be XFinSequence of D, n be Nat;
  hereby
    assume n in dom p;
    then n in dom FS2XFS (XFS2FS p);
    hence n+1 in dom XFS2FS p by Th13;
  end;
  assume n+1 in dom XFS2FS p;
  then n in dom FS2XFS (XFS2FS p) by Th13;
  hence thesis;
end;
