Ltac ssromega :=
  repeat arith_hypo_ssrnat2coqnat;
  arith_goal_ssrnat2coqnat; simpl;
  omega.Class monad (mon : Type -> Type) :=
  {
    ret : forall {A : Type},  A -> mon A;
    bind : forall {A B : Type}, mon A -> (A -> mon B) -> mon B
  }.Class monad (mon : Type -> Type) :=
  {
    ret : forall {A : Type},  A -> mon A;
    bind : forall {A B : Type}, mon A -> (A -> mon B) -> mon B
  }.Class monad (mon : Type -> Type) :=
  {
    ret : forall {A : Type},  A -> mon A;
    bind : forall {A B : Type}, mon A -> (A -> mon B) -> mon B
  }.Notation "'do!' X <- A ; B" := (bind A (fun X => B)) (at level 40).

Lemma forall_and: forall {A : Type} (f g : A -> Prop), (forall x : A, f x /\ g x) <-> (forall x : A, f x) /\ (forall x : A, g x).