
theory IntReal
  use int.Int
  use real.RealInfix
  use real.FromInt
  use real.Truncate

  goal G1 : from_int 2 = 2.0
  goal G2 : floor 1.5 = 1
  goal G3 : ceil 1.5 = 2
  goal G4 : floor (-. 1.5) = -2
  goal G5 : ceil (-. 1.5) = -1
  goal G6 : forall x : real. floor x <= ceil x
  goal G7 : forall x : real. floor x < ceil x -> from_int (floor x) <> x
end