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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/4533.v
parent53929e9bacf251f60c85d4ff24d46fec2c42ab4b (diff)
rename test files (do not start by a digit)
Diffstat (limited to 'test-suite/bugs/closed/4533.v')
-rw-r--r--test-suite/bugs/closed/4533.v230
1 files changed, 0 insertions, 230 deletions
diff --git a/test-suite/bugs/closed/4533.v b/test-suite/bugs/closed/4533.v
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index fd2380a070..0000000000
--- a/test-suite/bugs/closed/4533.v
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-(* -*- mode: coq; coq-prog-args: ("-nois" "-indices-matter" "-R" "." "Top" "-top" "bug_lex_wrong_rewrite_02") -*- *)
-(* File reduced by coq-bug-finder from original input, then from 1125 lines to
-346 lines, then from 360 lines to 346 lines, then from 822 lines to 271 lines,
-then from 285 lines to 271 lines *)
-(* coqc version 8.5 (January 2016) compiled on Jan 23 2016 16:15:22 with OCaml
-4.01.0
- coqtop version 8.5 (January 2016) *)
-Declare ML Module "ltac_plugin".
-Inductive False := .
-Axiom proof_admitted : False.
-Tactic Notation "admit" := case proof_admitted.
-Require Coq.Init.Datatypes.
-Import Coq.Init.Notations.
-Global Set Universe Polymorphism.
-Global Set Primitive Projections.
-Notation "A -> B" := (forall (_ : A), B) : type_scope.
-Module Export Datatypes.
- Set Implicit Arguments.
- Notation nat := Coq.Init.Datatypes.nat.
- Notation O := Coq.Init.Datatypes.O.
- Notation S := Coq.Init.Datatypes.S.
- Notation one := (S O).
- Notation two := (S one).
- Record prod (A B : Type) := pair { fst : A ; snd : B }.
- Notation "x * y" := (prod x y) : type_scope.
- Delimit Scope nat_scope with nat.
- Open Scope nat_scope.
-End Datatypes.
-Module Export Specif.
- Set Implicit Arguments.
- Record sig {A} (P : A -> Type) := exist { proj1_sig : A ; proj2_sig : P
-proj1_sig }.
- Notation sigT := sig (only parsing).
- Notation "{ x : A & P }" := (sigT (fun x:A => P)) : type_scope.
- Notation projT1 := proj1_sig (only parsing).
- Notation projT2 := proj2_sig (only parsing).
-End Specif.
-Global Set Keyed Unification.
-Global Unset Strict Universe Declaration.
-Definition Type1@{i} := Eval hnf in let gt := (Set : Type@{i}) in Type@{i}.
-Definition Type2@{i j} := Eval hnf in let gt := (Type1@{j} : Type@{i}) in
-Type@{i}.
-Definition Type2le@{i j} := Eval hnf in let gt := (Set : Type@{i}) in
- let ge := ((fun x => x) : Type1@{j} ->
-Type@{i}) in Type@{i}.
-Notation idmap := (fun x => x).
-Delimit Scope function_scope with function.
-Delimit Scope path_scope with path.
-Delimit Scope fibration_scope with fibration.
-Open Scope fibration_scope.
-Open Scope function_scope.
-Notation pr1 := projT1.
-Notation pr2 := projT2.
-Notation "x .1" := (pr1 x) (at level 3, format "x '.1'") : fibration_scope.
-Notation "x .2" := (pr2 x) (at level 3, format "x '.2'") : fibration_scope.
-Notation compose := (fun g f x => g (f x)).
-Notation "g 'o' f" := (compose g%function f%function) (at level 40, left
-associativity) : function_scope.
-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.
-Definition inverse {A : Type} {x y : A} (p : x = y) : y = x
- := match p with idpath => idpath end.
-Definition concat {A : Type} {x y z : A} (p : x = y) (q : y = z) : x = z :=
- match p, q with idpath, idpath => idpath end.
-Notation "1" := idpath : path_scope.
-Notation "p @ q" := (concat p%path q%path) (at level 20) : path_scope.
-Notation "p ^" := (inverse p%path) (at level 3, format "p '^'") : 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 pointwise_paths {A} {P:A->Type} (f g:forall x:A, P x)
- := forall x:A, f x = g x.
-Notation "f == g" := (pointwise_paths f g) (at level 70, no associativity) :
-type_scope.
-Definition Sect {A B : Type} (s : A -> B) (r : B -> A) :=
- forall x : A, r (s x) = x.
-Class IsEquiv {A B : Type} (f : A -> B) := BuildIsEquiv {
- equiv_inv : B -> A ;
- eisretr : Sect equiv_inv f;
- eissect : Sect f equiv_inv;
- eisadj : forall x : A, eisretr
-(f x) = ap f (eissect x)
- }.
-Arguments eissect {A B}%type_scope f%function_scope {_} _.
-Inductive Unit : Type1 := tt : Unit.
-Local Open Scope path_scope.
-Definition concat_p_pp {A : Type} {x y z t : A} (p : x = y) (q : y = z) (r : z
-= t) :
- p @ (q @ r) = (p @ q) @ r :=
- match r with idpath =>
- match q with idpath =>
- match p with idpath => 1
- end end end.
-Section Adjointify.
- Context {A B : Type} (f : A -> B) (g : B -> A).
- Context (isretr : Sect g f) (issect : Sect f g).
- Let issect' := fun x =>
- ap g (ap f (issect x)^) @ ap g (isretr (f x)) @ issect x.
-
- Let is_adjoint' (a : A) : isretr (f a) = ap f (issect' a).
- admit.
- Defined.
-
- Definition isequiv_adjointify : IsEquiv f
- := BuildIsEquiv A B f g isretr issect' is_adjoint'.
-End Adjointify.
-Definition ExtensionAlong {A B : Type} (f : A -> B)
- (P : B -> Type) (d : forall x:A, P (f x))
- := { s : forall y:B, P y & forall x:A, s (f x) = d x }.
-Fixpoint ExtendableAlong@{i j k l}
- (n : nat) {A : Type@{i}} {B : Type@{j}}
- (f : A -> B) (C : B -> Type@{k}) : Type@{l}
- := match n with
- | O => Unit@{l}
- | S n => (forall (g : forall a, C (f a)),
- ExtensionAlong@{i j k l l} f C g) *
- forall (h k : forall b, C b),
- ExtendableAlong n f (fun b => h b = k b)
- end.
-
-Definition ooExtendableAlong@{i j k l}
- {A : Type@{i}} {B : Type@{j}}
- (f : A -> B) (C : B -> Type@{k}) : Type@{l}
- := forall n, ExtendableAlong@{i j k l} n f C.
-
-Module Type ReflectiveSubuniverses.
-
- Parameter ReflectiveSubuniverse@{u a} : Type2@{u a}.
-
- Parameter O_reflector@{u a i} : forall (O : ReflectiveSubuniverse@{u a}),
- Type2le@{i a} -> Type2le@{i a}.
-
- Parameter In@{u a i} : forall (O : ReflectiveSubuniverse@{u a}),
- Type2le@{i a} -> Type2le@{i a}.
-
- Parameter O_inO@{u a i} : forall (O : ReflectiveSubuniverse@{u a}) (T :
-Type@{i}),
- In@{u a i} O (O_reflector@{u a i} O T).
-
- Parameter to@{u a i} : forall (O : ReflectiveSubuniverse@{u a}) (T :
-Type@{i}),
- T -> O_reflector@{u a i} O T.
-
- Parameter extendable_to_O@{u a i j k}
- : forall (O : ReflectiveSubuniverse@{u a}) {P : Type2le@{i a}} {Q :
-Type2le@{j a}} {Q_inO : In@{u a j} O Q},
- ooExtendableAlong@{i i j k} (to O P) (fun _ => Q).
-
-End ReflectiveSubuniverses.
-
-Module ReflectiveSubuniverses_Theory (Os : ReflectiveSubuniverses).
- Export Os.
- Existing Class In.
- Module Export Coercions.
- Coercion O_reflector : ReflectiveSubuniverse >-> Funclass.
- End Coercions.
- Global Existing Instance O_inO.
-
- Section ORecursion.
- Context {O : ReflectiveSubuniverse}.
-
- Definition O_rec {P Q : Type} {Q_inO : In O Q}
- (f : P -> Q)
- : O P -> Q
- := (fst (extendable_to_O O one) f).1.
-
- Definition O_rec_beta {P Q : Type} {Q_inO : In O Q}
- (f : P -> Q) (x : P)
- : O_rec f (to O P x) = f x
- := (fst (extendable_to_O O one) f).2 x.
-
- Definition O_indpaths {P Q : Type} {Q_inO : In O Q}
- (g h : O P -> Q) (p : g o to O P == h o to O P)
- : g == h
- := (fst (snd (extendable_to_O O two) g h) p).1.
-
- End ORecursion.
-
-
- Section Reflective_Subuniverse.
- Context (O : ReflectiveSubuniverse@{Ou Oa}).
-
- Definition isequiv_to_O_inO@{u a i} (T : Type@{i}) `{In@{u a i} O T} :
-IsEquiv@{i i} (to O T).
- Proof.
-
- pose (g := O_rec@{u a i i i i i} idmap).
- refine (isequiv_adjointify (to O T) g _ _).
- -
- refine (O_indpaths@{u a i i i i i} (to O T o g) idmap _).
- intros x.
- apply ap.
- apply O_rec_beta.
- -
- intros x.
- apply O_rec_beta.
- Defined.
- Global Existing Instance isequiv_to_O_inO.
-
- End Reflective_Subuniverse.
-
-End ReflectiveSubuniverses_Theory.
-
-Module Type Preserves_Fibers (Os : ReflectiveSubuniverses).
- Module Export Os_Theory := ReflectiveSubuniverses_Theory Os.
-End Preserves_Fibers.
-
-Opaque eissect.
-Module Lex_Reflective_Subuniverses
- (Os : ReflectiveSubuniverses) (Opf : Preserves_Fibers Os).
- Import Opf.
- Goal forall (O : ReflectiveSubuniverse) (A : Type) (B : A -> Type) (A_inO :
-In O A),
-
- forall g,
- forall (x : O {x : A & B x}) v v' v'' (p2 : v'' = v') (p0 : v' = v) (p1 :
-v = _) r,
- (p2
- @ (p0
- @ p1))
- @ eissect (to O A) (g x) = r.
- intros.
- cbv zeta.
- rewrite concat_p_pp.
- match goal with
- | [ |- p2 @ p0 @ p1 @ eissect (to O A) (g x) = r ] => idtac "good"
- | [ |- ?G ] => fail 1 "bad" G
- end.
- Fail rewrite concat_p_pp.