diff options
| author | Vincent Laporte | 2018-10-02 13:44:46 +0000 |
|---|---|---|
| committer | Vincent Laporte | 2018-10-04 08:01:34 +0000 |
| commit | db22ae6140259dd065fdd80af4cb3c3bab41c184 (patch) | |
| tree | e17ad7016014a4e2dd4001d826575342c2812fc3 /test-suite/bugs/closed/3422.v | |
| parent | 53929e9bacf251f60c85d4ff24d46fec2c42ab4b (diff) | |
rename test files (do not start by a digit)
Diffstat (limited to 'test-suite/bugs/closed/3422.v')
| -rw-r--r-- | test-suite/bugs/closed/3422.v | 209 |
1 files changed, 0 insertions, 209 deletions
diff --git a/test-suite/bugs/closed/3422.v b/test-suite/bugs/closed/3422.v deleted file mode 100644 index 460ae8f110..0000000000 --- a/test-suite/bugs/closed/3422.v +++ /dev/null @@ -1,209 +0,0 @@ -Require Import TestSuite.admit. -Generalizable All Variables. -Set Implicit Arguments. -Set Universe Polymorphism. -Axiom admit : forall {T}, T. -Reserved Infix "o" (at level 40, left associativity). -Class IsEquiv {A B : Type} (f : A -> B) := { equiv_inv : B -> A }. -Record Equiv A B := { equiv_fun :> A -> B ; equiv_isequiv :> IsEquiv equiv_fun }. -Existing Instance equiv_isequiv. -Delimit Scope equiv_scope with equiv. -Local Open Scope equiv_scope. -Notation "A <~> B" := (Equiv A B) (at level 85) : equiv_scope. -Notation "f ^-1" := (@equiv_inv _ _ f _) (at level 3) : equiv_scope. -Axiom IsHSet : Type -> Type. -Existing Class IsHSet. -Definition trunc_equiv' `(f : A <~> B) `{IsHSet A} : IsHSet B := admit. -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); - - trunc_morphism : forall s d, IsHSet (morphism s d) }. - -Bind Scope category_scope with PreCategory. -Infix "o" := (@compose _ _ _ _) : morphism_scope. - -Delimit Scope functor_scope with functor. - -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) - }. - -Bind Scope functor_scope with Functor. -Arguments morphism_of [C%category] [D%category] F%functor [s%object d%object] m%morphism : rename, simpl nomatch. -Notation "F '_1' m" := (morphism_of F m) (at level 10, no associativity) : morphism_scope. -Local Open Scope morphism_scope. - -Class IsIsomorphism {C : PreCategory} {s d} (m : morphism C s d) := { morphism_inverse : morphism C d s }. - -Local Notation "m ^-1" := (morphism_inverse (m := m)) : morphism_scope. - -Class Isomorphic {C : PreCategory} s d := - { - morphism_isomorphic :> morphism C s d; - isisomorphism_isomorphic :> IsIsomorphism morphism_isomorphic - }. - -Coercion morphism_isomorphic : Isomorphic >-> morphism. - -Local Infix "<~=~>" := Isomorphic (at level 70, no associativity) : category_scope. - -Definition isisomorphism_inverse `(@IsIsomorphism C x y m) : IsIsomorphism m^-1 := {| morphism_inverse := m |}. - -Global Instance isisomorphism_compose `(@IsIsomorphism C y z m0) `(@IsIsomorphism C x y m1) -: IsIsomorphism (m0 o m1). -admit. -Defined. - -Section composition. - Variable C : PreCategory. - Variable D : PreCategory. - Variable E : PreCategory. - Variable G : Functor D E. - Variable F : Functor C D. - - Definition composeF : Functor C E - := Build_Functor - C E - (fun c => G (F c)) - (fun _ _ m => morphism_of G (morphism_of F m)). -End composition. -Infix "o" := composeF : functor_scope. - -Delimit Scope natural_transformation_scope with natural_transformation. -Record NaturalTransformation C D (F G : Functor C D) := { components_of :> forall c, morphism D (F c) (G c) }. - -Section compose. - Variable C : PreCategory. - Variable D : PreCategory. - Variables F F' F'' : Functor C D. - - Variable T' : NaturalTransformation F' F''. - Variable T : NaturalTransformation F F'. - - Local Notation CO c := (T' c o T c). - - Definition composeT - : NaturalTransformation F F'' := Build_NaturalTransformation F F'' (fun c => CO c). - -End compose. - -Section whisker. - Variable C : PreCategory. - Variable D : PreCategory. - Variable E : PreCategory. - - Section L. - Variable F : Functor D E. - Variables G G' : Functor C D. - Variable T : NaturalTransformation G G'. - - Local Notation CO c := (morphism_of F (T c)). - - Definition whisker_l - := Build_NaturalTransformation - (F o G) (F o G') - (fun c => CO c). - - End L. - - Section R. - Variables F F' : Functor D E. - Variable T : NaturalTransformation F F'. - Variable G : Functor C D. - - Local Notation CO c := (T (G c)). - - Definition whisker_r - := Build_NaturalTransformation - (F o G) (F' o G) - (fun c => CO c). - End R. -End whisker. -Infix "o" := composeT : natural_transformation_scope. -Infix "oL" := whisker_l (at level 40, left associativity) : natural_transformation_scope. -Infix "oR" := whisker_r (at level 40, left associativity) : natural_transformation_scope. - -Section path_natural_transformation. - - Variable C : PreCategory. - Variable D : PreCategory. - Variables F G : Functor C D. - - Lemma equiv_sig_natural_transformation - : { CO : forall x, morphism D (F x) (G x) - | forall s d (m : morphism C s d), - CO d o F _1 m = G _1 m o CO s } - <~> NaturalTransformation F G. - admit. - Defined. - - Global Instance trunc_natural_transformation - : IsHSet (NaturalTransformation F G). - Proof. - eapply trunc_equiv'; [ exact equiv_sig_natural_transformation | ]. - admit. - Qed. - -End path_natural_transformation. -Definition functor_category (C D : PreCategory) : PreCategory - := @Build_PreCategory (Functor C D) (@NaturalTransformation C D) (@composeT C D) _. - -Notation "C -> D" := (functor_category C D) : category_scope. - -Definition NaturalIsomorphism (C D : PreCategory) F G := @Isomorphic (C -> D) F G. - -Coercion natural_transformation_of_natural_isomorphism C D F G (T : @NaturalIsomorphism C D F G) : NaturalTransformation F G - := T : morphism _ _ _. -Local Infix "<~=~>" := NaturalIsomorphism : natural_transformation_scope. -Global Instance isisomorphism_compose' - `(T' : @NaturalTransformation C D F' F'') - `(T : @NaturalTransformation C D F F') - `{@IsIsomorphism (C -> D) F' F'' T'} - `{@IsIsomorphism (C -> D) F F' T} -: @IsIsomorphism (C -> D) F F'' (T' o T)%natural_transformation - := @isisomorphism_compose (C -> D) _ _ T' _ _ T _. - -Section lemmas. - Local Open Scope natural_transformation_scope. - - Variable C : PreCategory. - Variable F : C -> PreCategory. - Context - {w x y z} - {f : Functor (F w) (F z)} {f0 : Functor (F w) (F y)} - {f1 : Functor (F x) (F y)} {f2 : Functor (F y) (F z)} - {f3 : Functor (F w) (F x)} {f4 : Functor (F x) (F z)} - {f5 : Functor (F w) (F z)} {n : f5 <~=~> (f4 o f3)%functor} - {n0 : f4 <~=~> (f2 o f1)%functor} {n1 : f0 <~=~> (f1 o f3)%functor} - {n2 : f <~=~> (f2 o f0)%functor}. - - Lemma p_composition_of_coherent_iso_for_rewrite__isisomorphism_helper' - : @IsIsomorphism - (_ -> _) _ _ - (n2 ^-1 o (f2 oL n1 ^-1 o (admit o (n0 oR f3 o n))))%natural_transformation. - Proof. - eapply isisomorphism_compose'; - [ eapply isisomorphism_inverse - | eapply isisomorphism_compose'; - [ admit - | eapply isisomorphism_compose'; - [ admit | - eapply isisomorphism_compose'; [ admit | ]]]]. - Set Printing All. Set Printing Universes. - apply @isisomorphism_isomorphic. - Qed. - -End lemmas. |
