theory Test_simplify_array
  use int.Int
  use map.Map
  goal G1 : forall x y:int. forall m: map int int.
    get (set m y x) y = x
  goal G2 : forall x y z t:int. forall m: map int int.
    z <> x ->
    get m z = y ->
    get (set m x t) z = y
  goal G3 : forall y t:int. forall m: map int int.
    get m 0 = y ->
    get (set m 1 t) 0 = y
  goal G4 : forall x y:int. forall m: map int int.
    get (set (set m 1 y) 0 x) 1 = y
end
