update after changes in Lean
This commit is contained in:
Floris van Doorn
parent
da033c0f4c
commit
e019097fed
3 changed files with 6 additions and 67 deletions
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@ -31,7 +31,7 @@ begin
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{ apply is_conn_fun_trunc_elim, apply is_conn_fun_tr },
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{ have is_trunc (n+1) (ptrunc n.+1 A), from !is_trunc_trunc,
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have is_trunc ((n+1).+1) (ptrunc n A), by do 2 apply is_trunc_succ, apply is_trunc_trunc,
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apply is_trunc_pfiber }
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exact is_trunc_pfiber _ _ _ _ }
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end
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end
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@ -673,7 +673,7 @@ namespace EM
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open fiber
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definition is_trunc_fiber_EM1_functor {G H : Group} (φ : G →g H) :
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is_trunc 1 (pfiber (EM1_functor φ)) :=
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!is_trunc_fiber
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is_trunc_pfiber _ _ _ _
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definition is_conn_fiber_EM1_functor {G H : Group} (φ : G →g H) :
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is_conn -1 (pfiber (EM1_functor φ)) :=
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@ -683,9 +683,7 @@ namespace EM
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definition is_trunc_fiber_EMadd1_functor {G H : AbGroup} (φ : G →g H) (n : ℕ) :
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is_trunc (n+1) (pfiber (EMadd1_functor φ n)) :=
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begin
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apply is_trunc_fiber
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end
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is_trunc_pfiber _ _ _ _
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definition is_conn_fiber_EMadd1_functor {G H : AbGroup} (φ : G →g H) (n : ℕ) :
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is_conn (n.-1) (pfiber (EMadd1_functor φ n)) :=
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@ -696,9 +694,7 @@ namespace EM
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definition is_trunc_fiber_EM_functor {G H : AbGroup} (φ : G →g H) (n : ℕ) :
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is_trunc n (pfiber (EM_functor φ n)) :=
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begin
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apply is_trunc_fiber
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end
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is_trunc_pfiber _ _ _ _
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definition is_conn_fiber_EM_functor {G H : AbGroup} (φ : G →g H) (n : ℕ) :
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is_conn (n.-2) (pfiber (EM_functor φ n)) :=
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@ -1651,7 +1651,7 @@ open is_trunc
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sigma_assoc_equiv_left _ (sigma_homotopy_constant_equiv pt (f pt))⁻¹ᵉ ⬝e
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sigma_equiv_sigma_right (λh₂,
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sigma_equiv_sigma_right (λr₂,
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sigma_equiv_sigma_right (λh₁, !comm_equiv_nondep) ⬝e !sigma_comm_equiv) ⬝e
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sigma_equiv_sigma_right (λh₁, !comm_equiv_constant) ⬝e !sigma_comm_equiv) ⬝e
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!sigma_comm_equiv) ⬝e
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!sigma_comm_equiv ⬝e
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sigma_equiv_sigma_right (λr,
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@ -1661,7 +1661,7 @@ open is_trunc
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sigma_equiv_sigma_left (pi_equiv_pi_right (λa, equiv_eq_closed_right _ r)) ⬝e
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sigma_equiv_sigma_right (λh₁, !eq_equiv_con_inv_eq_idp⁻¹ᵉ)) ⬝e
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!sigma_comm_equiv ⬝e
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sigma_equiv_sigma_right (λh₁, !comm_equiv_nondep)) ⬝e
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sigma_equiv_sigma_right (λh₁, !comm_equiv_constant)) ⬝e
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!sigma_comm_equiv) ⬝e
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!sigma_comm_equiv ⬝e sigma_equiv_sigma_right (λh₁,
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!sigma_comm_equiv ⬝e sigma_equiv_sigma_right (λh₂,
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@ -1675,63 +1675,6 @@ open is_trunc
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definition dsmash_pelim_equiv' (B : A → Type*) (C : Type*) :
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ppmap (⋀ B) C ≃ Π*a, B a →** C :=
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dsmash_pelim_equiv B C ⬝e (ppi_equiv_dbpmap B (λa, C))⁻¹ᵉ
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exit
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definition dsmash_arrow_equiv2 [constructor] (B : A → Type*) (C : Type) :
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(⋀ B → C) ≃ Σ(f : Πa, B a → C) (c₀ : C) (p : Πa, f a pt = c₀) (q : Πb, f pt b = c₀), p pt = q pt :=
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begin
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fapply equiv.MK,
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{ intro f, exact ⟨λa b, f (dsmash.mk a b), f auxr, f auxl, (λa, ap f (gluel a), λb, ap f (gluer b))⟩ },
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{ intro x, exact dsmash.elim x.1 x.2.2.1 x.2.1 x.2.2.2.1 x.2.2.2.2 },
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{ intro x, induction x with f x, induction x with c₁ x, induction x with c₀ x, induction x with p₁ p₂,
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apply ap (dpair _), apply ap (dpair _), apply ap (dpair _), esimp,
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exact pair_eq (eq_of_homotopy (elim_gluel _ _)) (eq_of_homotopy (elim_gluer _ _)) },
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{ intro f, apply eq_of_homotopy, intro x, induction x, reflexivity, reflexivity, reflexivity,
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apply eq_pathover, apply hdeg_square, apply elim_gluel,
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apply eq_pathover, apply hdeg_square, apply elim_gluer }
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end
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definition dsmash_arrow_equiv2_inv_pt [constructor]
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(x : Σ(f : Πa, B a → C) (c₁ : C) (c₀ : C), (Πa, f a pt = c₀) × (Πb, f pt b = c₁)) :
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to_inv (dsmash_arrow_equiv B C) x pt = x.1 pt pt :=
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by reflexivity
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open pi
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definition dsmash_pmap_equiv2 (B : A → Type*) (C : Type*) :
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(⋀ B →* C) ≃ dbppmap B (λa, C) :=
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begin
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refine !pmap.sigma_char ⬝e _,
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refine sigma_equiv_sigma_left !dsmash_arrow_equiv ⬝e _,
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refine sigma_equiv_sigma_right (λx, equiv_eq_closed_left _ (dsmash_arrow_equiv_inv_pt x)) ⬝e _,
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refine !sigma_assoc_equiv ⬝e _,
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refine sigma_equiv_sigma_right (λf, !sigma_assoc_equiv ⬝e
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sigma_equiv_sigma_right (λc₁, !sigma_assoc_equiv ⬝e
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sigma_equiv_sigma_right (λc₂, sigma_equiv_sigma_left !sigma.equiv_prod⁻¹ᵉ ⬝e
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!sigma_assoc_equiv) ⬝e
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sigma_assoc_equiv_left _ (sigma_homotopy_constant_equiv pt (λa, f a pt))⁻¹ᵉ ⬝e
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sigma_equiv_sigma_right (λh₁, !sigma_comm_equiv) ⬝e !sigma_comm_equiv) ⬝e
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sigma_assoc_equiv_left _ (sigma_homotopy_constant_equiv pt (f pt))⁻¹ᵉ ⬝e
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sigma_equiv_sigma_right (λh₂,
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sigma_equiv_sigma_right (λr₂,
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sigma_equiv_sigma_right (λh₁, !comm_equiv_nondep) ⬝e !sigma_comm_equiv) ⬝e
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!sigma_comm_equiv) ⬝e
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!sigma_comm_equiv ⬝e
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sigma_equiv_sigma_right (λr,
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sigma_equiv_sigma_left (pi_equiv_pi_right (λb, equiv_eq_closed_right _ r)) ⬝e
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sigma_equiv_sigma_right (λh₂,
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sigma_equiv_sigma !eq_equiv_con_inv_eq_idp⁻¹ᵉ (λr₂,
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sigma_equiv_sigma_left (pi_equiv_pi_right (λa, equiv_eq_closed_right _ r)) ⬝e
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sigma_equiv_sigma_right (λh₁, !eq_equiv_con_inv_eq_idp⁻¹ᵉ)) ⬝e
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!sigma_comm_equiv ⬝e
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sigma_equiv_sigma_right (λh₁, !comm_equiv_nondep)) ⬝e
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!sigma_comm_equiv) ⬝e
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!sigma_comm_equiv ⬝e sigma_equiv_sigma_right (λh₁,
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!sigma_comm_equiv ⬝e sigma_equiv_sigma_right (λh₂,
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!sigma_sigma_eq_right))) ⬝e _,
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refine !sigma_assoc_equiv' ⬝e _,
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refine sigma_equiv_sigma_left (@sigma_pi_equiv_pi_sigma _ _ (λa f, f pt = pt) ⬝e
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pi_equiv_pi_right (λa, !pmap.sigma_char⁻¹ᵉ)) ⬝e _,
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exact !dbpmap.sigma_char⁻¹ᵉ
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end
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end dsmash
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