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Module Type SIG.
Inductive w : Set :=
A : w.
Parameter f : w -> w.
End SIG.
Module M : SIG.
Inductive w : Set :=
A : w.
Definition f x := match x with
| A => A
end.
End M.
Module N := M.
Check (N.f M.A).
(* Check use of equivalence on inductive types (bug #1242) *)
Module Type ASIG.
Inductive t : Set := a | b : t.
Definition f := fun x => match x with a => true | b => false end.
End ASIG.
Module Type BSIG.
Declare Module A : ASIG.
Definition f := fun x => match x with A.a => true | A.b => false end.
End BSIG.
Module C (A : ASIG) (B : BSIG with Module A:=A).
(* Check equivalence is considered in "case_info" *)
Lemma test : forall x, A.f x = B.f x.
intro x. unfold B.f, A.f.
destruct x; reflexivity.
Qed.
(* Check equivalence is considered in pattern-matching *)
Definition f (x : A.t) := match x with B.A.a => true | B.A.b => false end.
End C.
(* Check subtyping of the context of parameters of the inductive types *)
(* Only the number of expected uniform parameters and the convertibility *)
(* of the inductive arities and constructors types are checked *)
Module Type S. Inductive I (x:=0) (y:nat): Set := c: x=y -> I y. End S.
Module P : S. Inductive I (y':nat) (z:=y'): Set := c : 0=y' -> I y'. End P.
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