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(* File reduced by coq-bug-finder from original input, then from 1461 lines to 81 lines, then from 84 lines to 40 lines, then from 50 lines to 24 lines *)
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.
Class Contr_internal (A : Type) := BuildContr {
center : A ;
contr : (forall y : A, center = y)
}.
Class Funext := {}.
Definition path_forall `{Funext} {A : Type} {P : A -> Type} (f g : forall x : A, P x) :
(forall x, f x = g x) -> f = g.
Admitted.
Inductive Empty : Set := .
Fail Instance contr_from_Empty {_ : Funext} (A : Type) :
Contr_internal (Empty -> A) :=
BuildContr _
(Empty_rect (fun _ => A))
(fun f => path_forall _ f (fun x => Empty_rect _ x)).
Fail Instance contr_from_Empty {F : Funext} (A : Type) :
Contr_internal (Empty -> A) :=
BuildContr _
(Empty_rect (fun _ => A))
(fun f => path_forall _ f (fun x => Empty_rect _ x)).
(** This could be disallowed, this uses the Funext argument *)
Instance contr_from_Empty {_ : Funext} (A : Type) :
Contr_internal (Empty -> A) :=
BuildContr _
(Empty_rect (fun _ => A))
(fun f => path_forall _ f (fun x => Empty_rect (fun _ => _ x = f x) x)).
Instance contr_from_Empty' {_ : Funext} (A : Type) :
Contr_internal (Empty -> A) :=
BuildContr _
(Empty_rect (fun _ => A))
(fun f => path_forall _ f (fun x => Empty_rect (fun _ => _ x = f x) x)).
(* Toplevel input, characters 15-220:
Anomaly: unknown meta ?190. Please report. *)
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