reserve i, j, k, l, m, n, t for Nat;

theorem Th9:
  for i,j be non zero Nat holds i -' j < i
proof
  let i,j be non zero Nat;
  per cases;
  suppose
A1: j <= i;
    i - j < i - 0 by XREAL_1:15;
    hence thesis by A1,XREAL_1:233;
  end;
  suppose
    j > i;
    hence thesis by Th8;
  end;
end;
