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Set Universe Polymorphism.
Set Printing Universes.
Inductive type_paths (A : Type) : Type -> Prop
:= idtypepath : type_paths A A.
Monomorphic Definition comp_type_paths := Eval compute in type_paths.
Check comp_type_paths.
(* comp_type_paths
: Type (* Top.12 *) -> Type (* Top.12 *) -> Prop *)
(* This is terrible. *)
Inductive type_paths' (A : Type) : Type -> Prop
:= idtypepath' : type_paths' A A
| other_type_path : False -> forall B : Type, type_paths' A B.
Monomorphic Definition comp_type_paths' := Eval compute in type_paths'.
Check comp_type_paths'.
(* comp_type_paths'
: Type (* Top.24 *) -> Type (* Top.23 *) -> Prop *)
(* Ok, then ... *)
(** Fail if it's [U0 -> U0 -> _], but not on [U0 -> U1 -> _]. *)
Goal Type.
Proof.
match type of comp_type_paths' with
| ?U0 -> ?U1 -> ?R
=> exact (@comp_type_paths' nat U0)
end.
Defined.
Goal Type.
Proof.
Fail match type of comp_type_paths with
| ?U0 -> ?U1 -> ?R
=> exact (@comp_type_paths nat U0)
end.
(* Toplevel input, characters 110-112:
Error:
The term "Type (* Top.51 *)" has type "Type (* Top.51+1 *)"
while it is expected to have type "Type (* Top.51 *)"
(Universe inconsistency: Cannot enforce Top.51 < Top.51 because Top.51
= Top.51)). *)
admit.
Defined.
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