Class PrimaryBackupParams (base_params : BaseParams) :=
  {
    input_eq_dec : forall x y : input, {x = y} + {x <> y}
  }.Class PrimaryBackupParams (base_params : BaseParams) :=
  {
    input_eq_dec : forall x y : input, {x = y} + {x <> y}
  }.Inductive name := Primary | Backup.Inductive name := Primary | Backup.Inductive name := Primary | Backup.

Lemma name_eq_dec : forall x y : name, {x = y} + {x <> y}.