reserve i, j, m, n for Nat,
  z, B0 for set,
  f, x0 for real-valued FinSequence;

theorem Th6:
  for h being real-valued FinSequence st h is increasing holds for
  i,j being Nat st i<=j & 1<=i & j<=len h holds h.i <= h.j
proof
  let h be real-valued FinSequence;
  assume
A1: h is increasing;
  let i,j be Nat;
  assume that
A2: i<=j and
A3: 1<=i and
A4: j<=len h;
  i<j or i=j by A2,XXREAL_0:1;
  hence thesis by A1,A3,A4,Th5;
end;
