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|
Generalizable All Variables.
Inductive paths {A : Type} (a : A) : A -> Type :=
idpath : paths a a.
Notation "x = y :> A" := (@paths A x y) : type_scope.
Notation "x = y" := (x = y :>_) : type_scope.
Module success.
Axiom bar : nat -> Type -> Type.
Definition foo (n : nat) (A : Type) : Type :=
match n with
| O => A
| S n' => forall x y : A, bar n' (x = y)
end.
Definition foo_succ n A : foo (S n) A.
Admitted.
Goal forall n (X Y : Type) (y : X) (x : X), bar n (x = y).
intros.
apply (foo_succ _ _).
Defined.
End success.
Module failure.
Fixpoint bar (n : nat) (A : Type) : Type :=
match n with
| O => A
| S n' => forall x y : A, bar n' (x = y)
end.
Definition foo_succ n A : bar (S n) A.
Admitted.
Goal forall n (X Y : Type) (y : X) (x : X), bar n (x = y).
intros.
apply foo_succ.
(* Toplevel input, characters 22-34:
Error: In environment
n : nat
X : Type
Y : Type
y : X
x : X
Unable to unify
"forall x0 y0 : ?16,
(fix bar (n : nat) (A : Type) {struct n} : Type :=
match n with
| 0 => A
| S n' => forall x y : A, bar n' (x = y)
end) ?15 (x0 = y0)" with
"(fix bar (n : nat) (A : Type) {struct n} : Type :=
match n with
| 0 => A
| S n' => forall x y : A, bar n' (x = y)
end) n (x = y)".
*)
Defined.
End failure.
|
