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

theorem
  for x,y be Real st x >= 0 & y > 0 holds x / ( [\ x / y /] + 1 ) < y
proof
  let x,y be Real such that
A1: x >= 0 and
A2: y > 0;
  (x / y) * y < ( [\ x / y /] + 1 ) * y by A2,INT_1:29,XREAL_1:68;
  then
A3: x < ( [\ x / y /] + 1 ) * y by A2,XCMPLX_1:87;
  [\ x / y /] >= 0 by A1,A2,INT_1:53;
  hence thesis by A3,XREAL_1:83;
end;
