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+Lemma match_bool_fn b A B xT xF
+: match b as b return forall x : A, B b x with
+ | true => xT
+ | false => xF
+ end
+ = fun x : A => match b as b return B b x with
+ | true => xT x
+ | false => xF x
+ end.
+admit.
+Defined.
+Lemma match_bool_comm_1 (b : bool) A B (F : forall x : A, B x) t f
+: (if b as b return B (if b then t else f) then F t else F f)
+ = F (if b then t else f).
+admit.
+Defined.
+Hint Rewrite match_bool_fn : matchdb.
+Fail Hint Rewrite match_bool_comm_1 : matchdb.