feat(library): export [reducible] annotations from function namespace to top-level
see issue #433
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3 changed files with 18 additions and 13 deletions
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@ -18,23 +18,23 @@ definition compose [reducible] (f : B → C) (g : A → B) : A → C :=
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definition id [reducible] (a : A) : A :=
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a
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definition on_fun (f : B → B → C) (g : A → B) : A → A → C :=
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definition on_fun [reducible] (f : B → B → C) (g : A → B) : A → A → C :=
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λx y, f (g x) (g y)
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definition combine (f : A → B → C) (op : C → D → E) (g : A → B → D) : A → B → E :=
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definition combine [reducible] (f : A → B → C) (op : C → D → E) (g : A → B → D) : A → B → E :=
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λx y, op (f x y) (g x y)
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definition const {A : Type} (B : Type) (a : A) : B → A :=
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definition const [reducible] (B : Type) (a : A) : B → A :=
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λx, a
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definition dcompose {A : Type} {B : A → Type} {C : Π {x : A}, B x → Type}
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definition dcompose [reducible] {B : A → Type} {C : Π {x : A}, B x → Type}
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(f : Π {x : A} (y : B x), C y) (g : Πx, B x) : Πx, C (g x) :=
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λx, f (g x)
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definition flip {A : Type} {B : Type} {C : A → B → Type} (f : Πx y, C x y) : Πy x, C x y :=
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definition flip [reducible] {C : A → B → Type} (f : Πx y, C x y) : Πy x, C x y :=
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λy x, f x y
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definition app {A : Type} {B : A → Type} (f : Πx, B x) (x : A) : B x :=
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definition app [reducible] {B : A → Type} (f : Πx, B x) (x : A) : B x :=
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f x
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precedence `∘'`:60
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@ -53,3 +53,6 @@ notation f `-[` op `]-` g := combine f op g
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notation a `⟨` f `⟩` b := f a b
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end function
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-- copy reducible annotations to top-level
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export [reduce-hints] function
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@ -17,23 +17,23 @@ definition compose [reducible] (f : B → C) (g : A → B) : A → C :=
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definition id [reducible] (a : A) : A :=
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a
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definition on_fun (f : B → B → C) (g : A → B) : A → A → C :=
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definition on_fun [reducible] (f : B → B → C) (g : A → B) : A → A → C :=
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λx y, f (g x) (g y)
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definition combine (f : A → B → C) (op : C → D → E) (g : A → B → D) : A → B → E :=
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definition combine [reducible] (f : A → B → C) (op : C → D → E) (g : A → B → D) : A → B → E :=
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λx y, op (f x y) (g x y)
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definition const {A : Type} (B : Type) (a : A) : B → A :=
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definition const [reducible] (B : Type) (a : A) : B → A :=
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λx, a
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definition dcompose {A : Type} {B : A → Type} {C : Π {x : A}, B x → Type}
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definition dcompose [reducible] {B : A → Type} {C : Π {x : A}, B x → Type}
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(f : Π {x : A} (y : B x), C y) (g : Πx, B x) : Πx, C (g x) :=
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λx, f (g x)
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definition flip {A : Type} {B : Type} {C : A → B → Type} (f : Πx y, C x y) : Πy x, C x y :=
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definition flip [reducible] {C : A → B → Type} (f : Πx y, C x y) : Πy x, C x y :=
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λy x, f x y
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definition app {A : Type} {B : A → Type} (f : Πx, B x) (x : A) : B x :=
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definition app [reducible] {B : A → Type} (f : Πx, B x) (x : A) : B x :=
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f x
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precedence `∘'`:60
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@ -47,3 +47,6 @@ infixr $ := app
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notation f `-[` op `]-` g := combine f op g
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end function
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-- copy reducible annotations to top-level
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export [reduce-hints] function
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@ -94,7 +94,6 @@ namespace pi
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definition transport_V [reducible] (P : A → Type) {x y : A} (p : x = y) (u : P y) : P x :=
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p⁻¹ ▹ u
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open function
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protected definition functor_pi : (Π(a:A), B a) → (Π(a':A'), B' a') := (λg a', f1 a' (g (f0 a')))
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/- Equivalences -/
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definition isequiv_functor_pi [instance] (f0 : A' → A) (f1 : Π(a':A'), B (f0 a') → B' a')
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