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refactor: use notation for trunc_index

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Floris van Doorn 2018-09-20 16:03:32 +02:00
parent 3468ab8a9f
commit f2dfca25f9
2 changed files with 6 additions and 6 deletions
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6
hott/types/fiber.hlean
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@ -130,7 +130,7 @@ namespace fiber
end end
definition is_trunc_fiber (n : ℕ₋₂) {A B : Type} (f : A → B) (b : B) definition is_trunc_fiber (n : ℕ₋₂) {A B : Type} (f : A → B) (b : B)
[is_trunc n A] [is_trunc (n.+1) B] : is_trunc n (fiber f b) := (HA : is_trunc n A) (HB : is_trunc (n.+1) B) : is_trunc n (fiber f b) :=
is_trunc_equiv_closed_rev n !fiber.sigma_char _ is_trunc_equiv_closed_rev n !fiber.sigma_char _
definition is_contr_fiber_id (A : Type) (a : A) : is_contr (fiber (@id A) a) := definition is_contr_fiber_id (A : Type) (a : A) : is_contr (fiber (@id A) a) :=
@ -404,8 +404,8 @@ namespace fiber
end end
definition is_trunc_pfiber (n : ℕ₋₂) {A B : Type*} (f : A →* B) definition is_trunc_pfiber (n : ℕ₋₂) {A B : Type*} (f : A →* B)
[is_trunc n A] [is_trunc (n.+1) B] : is_trunc n (pfiber f) := (HA : is_trunc n A) (HB : is_trunc (n.+1) B) : is_trunc n (pfiber f) :=
is_trunc_fiber n f pt is_trunc_fiber n f pt HA HB
definition pfiber_pequiv_of_is_contr [constructor] {A B : Type*} (f : A →* B) (H : is_contr B) : definition pfiber_pequiv_of_is_contr [constructor] {A B : Type*} (f : A →* B) (H : is_contr B) :
pfiber f ≃* A := pfiber f ≃* A :=

6
hott/types/pi.hlean
View file

@ -274,7 +274,7 @@ namespace pi
/- Truncatedness: any dependent product of n-types is an n-type -/ /- Truncatedness: any dependent product of n-types is an n-type -/
theorem is_trunc_pi (B : A → Type) (n : trunc_index) theorem is_trunc_pi (B : A → Type) (n : ℕ₋₂)
[H : ∀a, is_trunc n (B a)] : is_trunc n (Πa, B a) := [H : ∀a, is_trunc n (B a)] : is_trunc n (Πa, B a) :=
begin begin
revert B H, revert B H,
@ -291,11 +291,11 @@ namespace pi
is_trunc_eq n (f a) (g a) } is_trunc_eq n (f a) (g a) }
end end
local attribute is_trunc_pi [instance] local attribute is_trunc_pi [instance]
theorem is_trunc_pi_eq (n : trunc_index) (f g : Πa, B a) theorem is_trunc_pi_eq (n : ℕ₋₂) (f g : Πa, B a)
[H : ∀a, is_trunc n (f a = g a)] : is_trunc n (f = g) := [H : ∀a, is_trunc n (f a = g a)] : is_trunc n (f = g) :=
is_trunc_equiv_closed_rev n !eq_equiv_homotopy _ is_trunc_equiv_closed_rev n !eq_equiv_homotopy _
theorem is_trunc_not [instance] (n : trunc_index) (A : Type) : is_trunc (n.+1) ¬A := theorem is_trunc_not [instance] (n : ℕ₋₂) (A : Type) : is_trunc (n.+1) ¬A :=
by unfold not;exact _ by unfold not;exact _
theorem is_prop_pi_eq [instance] [priority 490] (a : A) : is_prop (Π(a' : A), a = a') := theorem is_prop_pi_eq [instance] [priority 490] (a : A) : is_prop (Π(a' : A), a = a') :=