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+Inductive type : Set :=
+ Tptr : type -> type
+ | Tref : type -> type
+ | Trv_ref : type -> type
+ | Tint : type -> type -> type
+ | Tvoid : type
+ | Tarray : type -> type -> type
+ | Tnamed : type -> type
+ | Tfunction : type -> type -> type -> type
+ | Tbool : type
+ | Tmember_pointer : type -> type -> type
+ | Tfloat : type -> type
+ | Tqualified : type -> type -> type
+ | Tnullptr : type
+ | Tarch : type -> type -> type
+.
+Definition type_eq_dec : forall (ty1 ty2 : type), { ty1 = ty2 } + { ty1 <> ty2 }.
+Proof. fix IHty1 1. decide equality. Defined.
+
+Goal (if type_eq_dec (Tptr Tvoid) (Tptr Tvoid) then True else False).
+Proof.
+timeout 1 cbn.
+constructor.
+Qed.