import data.nat
open algebra

constant f {A : Type} : A → A → A

theorem test1 {A : Type} [s : comm_ring A] (a b c : A) (H : a + 0 = 0) : f a a = f 0 0 :=
begin
  rewrite add_zero at H,
  rewrite H
end

theorem test2 {A : Type} [s : comm_ring A] (a b c : A) (H : a + 0 = 0) : f a a = f 0 0 :=
begin
  rewrite add_zero at *,
  rewrite H
end

theorem test3 {A : Type} [s : comm_ring A] (a b c : A) (H : a + 0 = 0 + 0) : f a a = f 0 0 :=
begin
  rewrite add_zero at H,
  rewrite zero_add at H,
  rewrite H
end