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authorVincent Laporte2018-10-02 13:44:46 +0000
committerVincent Laporte2018-10-04 08:01:34 +0000
commitdb22ae6140259dd065fdd80af4cb3c3bab41c184 (patch)
treee17ad7016014a4e2dd4001d826575342c2812fc3 /test-suite/bugs/closed/3422.v
parent53929e9bacf251f60c85d4ff24d46fec2c42ab4b (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.v209
1 files changed, 0 insertions, 209 deletions
diff --git a/test-suite/bugs/closed/3422.v b/test-suite/bugs/closed/3422.v
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-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.