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authorGravatar Jason Gross <jgross@mit.edu>2014-05-09 10:13:32 -0400
committerGravatar Matthieu Sozeau <mattam@mattam.org>2014-05-10 15:39:39 +0200
commitc7284415e4bdd3315c84c7d15d140d3fee000bc5 (patch)
treecc8ded3feba7e1da0dd4f7d17b7e5f974de752c3 /test-suite/bugs/closed/HoTT_coq_064.v
parent3f64bd23a343bcd7be0ef07afa7d9e3249df24ec (diff)
Move opened bugs to bugs/opened
Diffstat (limited to 'test-suite/bugs/closed/HoTT_coq_064.v')
-rw-r--r--test-suite/bugs/closed/HoTT_coq_064.v187
1 files changed, 0 insertions, 187 deletions
diff --git a/test-suite/bugs/closed/HoTT_coq_064.v b/test-suite/bugs/closed/HoTT_coq_064.v
deleted file mode 100644
index fae954f81..000000000
--- a/test-suite/bugs/closed/HoTT_coq_064.v
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@@ -1,187 +0,0 @@
-(* File reduced by coq-bug-finder from 279 lines to 219 lines. *)
-
-Set Implicit Arguments.
-Set Universe Polymorphism.
-Definition admit {T} : T.
-Admitted.
-Module Export Overture.
- Reserved Notation "g 'o' f" (at level 40, left associativity).
-
- Inductive paths {A : Type} (a : A) : A -> Type :=
- idpath : paths a a.
-
- Arguments idpath {A a} , [A] a.
-
- Notation "x = y :> A" := (@paths A x y) : type_scope.
-
- Notation "x = y" := (x = y :>_) : type_scope.
-
- Delimit Scope path_scope with path.
-
- Local Open Scope path_scope.
-
- Definition ap {A B:Type} (f:A -> B) {x y:A} (p:x = y) : f x = f y
- := match p with idpath => idpath end.
-
- Definition apD10 {A} {B:A->Type} {f g : forall x, B x} (h:f=g)
- : forall x, f x = g x
- := fun x => match h with idpath => idpath end.
-
- Class IsEquiv {A B : Type} (f : A -> B) := BuildIsEquiv { equiv_inv : B -> A }.
-
- Delimit Scope equiv_scope with equiv.
- Local Open Scope equiv_scope.
-
- Notation "f ^-1" := (@equiv_inv _ _ f _) (at level 3) : equiv_scope.
-
- Class Funext :=
- { isequiv_apD10 :> forall (A : Type) (P : A -> Type) f g, IsEquiv (@apD10 A P f g) }.
-
- Definition path_forall `{Funext} {A : Type} {P : A -> Type} (f g : forall x : A, P x) :
- (forall x, f x = g x) -> f = g
- :=
- (@apD10 A P f g)^-1.
-
-End Overture.
-
-Module Export Core.
-
- Set Implicit Arguments.
- Delimit Scope morphism_scope with morphism.
- Delimit Scope category_scope with category.
- Delimit Scope object_scope with object.
-
- Record PreCategory :=
- {
- object :> Type;
- morphism : object -> object -> Type;
-
- compose : forall s d d',
- morphism d d'
- -> morphism s d
- -> morphism s d'
- where "f 'o' g" := (compose f g);
-
- associativity : forall x1 x2 x3 x4
- (m1 : morphism x1 x2)
- (m2 : morphism x2 x3)
- (m3 : morphism x3 x4),
- (m3 o m2) o m1 = m3 o (m2 o m1)
- }.
- Bind Scope category_scope with PreCategory.
- Arguments compose [!C%category s%object d%object d'%object] m1%morphism m2%morphism : rename.
-
- Infix "o" := compose : morphism_scope.
-
-End Core.
-
-Local Open Scope morphism_scope.
-Record Functor (C D : PreCategory) :=
- {
- object_of :> C -> D;
- morphism_of : forall s d, morphism C s d
- -> morphism D (object_of s) (object_of d)
- }.
-
-Inductive Unit : Set :=
- tt : Unit.
-
-Definition indiscrete_category (X : Type) : PreCategory
- := @Build_PreCategory X
- (fun _ _ => Unit)
- (fun _ _ _ _ _ => tt)
- (fun _ _ _ _ _ _ _ => idpath).
-
-
-Record NaturalTransformation C D (F G : Functor C D) := { components_of :> forall c, morphism D (F c) (G c) }.
-Section path_natural_transformation.
- Context `{Funext}.
- Variable C : PreCategory.
- Variable D : PreCategory.
- Variables F G : Functor C D.
-
- Section path.
- Variables T U : NaturalTransformation F G.
- Lemma path'_natural_transformation
- : components_of T = components_of U
- -> T = U.
- admit.
- Defined.
- Lemma path_natural_transformation
- : (forall x, T x = U x)
- -> T = U.
- Proof.
- intros.
- apply path'_natural_transformation.
- apply path_forall; assumption.
- Qed.
- End path.
-End path_natural_transformation.
-Ltac path_natural_transformation :=
- repeat match goal with
- | _ => intro
- | _ => apply path_natural_transformation; simpl
- end.
-Definition comma_category A B C (S : Functor A C) (T : Functor B C)
-: PreCategory.
- admit.
-Defined.
-Definition compose C D (F F' F'' : Functor C D)
- (T' : NaturalTransformation F' F'') (T : NaturalTransformation F F')
-: NaturalTransformation F F''
- := Build_NaturalTransformation F F''
- (fun c => T' c o T c).
-
-Infix "o" := compose : natural_transformation_scope.
-
-Local Open Scope natural_transformation_scope.
-
-Definition associativity `{fs : Funext}
- C D F G H I
- (V : @NaturalTransformation C D F G)
- (U : @NaturalTransformation C D G H)
- (T : @NaturalTransformation C D H I)
-: (T o U) o V = T o (U o V).
-Proof.
- path_natural_transformation.
-
- apply associativity.
-Qed.
-Definition functor_category `{Funext} (C D : PreCategory) : PreCategory
- := @Build_PreCategory (Functor C D)
- (@NaturalTransformation C D)
- (@compose C D)
- (@associativity _ C D).
-
-Notation "C -> D" := (functor_category C D) : category_scope.
-
-Definition compose_functor `{Funext} (C D E : PreCategory) : object ((C -> D) -> ((D -> E) -> (C -> E))).
- admit.
-
-Defined.
-
-Definition pullback_along `{Funext} (C C' D : PreCategory) (p : Functor C C')
-: object ((C' -> D) -> (C -> D))
- := Eval hnf in compose_functor _ _ _ p.
-
-Definition IsColimit `{Funext} C D (F : Functor D C) (x : object
- (@comma_category (indiscrete_category Unit)
- (@functor_category H (indiscrete_category Unit) C)
- (@functor_category H D C)
- admit
- (@pullback_along H D (indiscrete_category Unit) C
- admit))) : Type
- := admit.
-
-Generalizable All Variables.
-Axiom fs : Funext.
-
-Section bar.
-
- Variable D : PreCategory.
-
- Context `(has_colimits
- : forall F : Functor D C,
- @IsColimit _ C D F (colimits F)).
-(* Error: Unsatisfied constraints: Top.3773 <= Set
- (maybe a bugged tactic). *)