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+(* These always worked. *)
+Goal prod True True. firstorder. Qed.
+Goal True -> @sigT True (fun _ => True). firstorder. Qed.
+Goal prod True True. dtauto. Qed.
+Goal prod True True. tauto. Qed.
+
+(* These should work. *)
+Goal @sigT True (fun _ => True). dtauto. Qed.
+(* These should work, but don't *)
+(* Goal @sigT True (fun _ => True). firstorder. Qed. *)
+(* Goal @sigT True (fun _ => True). tauto. Qed. *)