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Seal several definitions as theorems.

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favonia 2017-06-06 23:10:25 -06:00
parent 18ee7ce410
commit 5fdc8ad2c8
1 changed files with 3 additions and 3 deletions
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6
homology/homology.hlean
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@ -24,12 +24,12 @@ namespace homology
parameter (theory : homology_theory) parameter (theory : homology_theory)
open homology_theory open homology_theory
definition HH_base_indep (n : ℤ) {A : Type} (a b : A) theorem HH_base_indep (n : ℤ) {A : Type} (a b : A)
: HH theory n (pType.mk A a) ≃g HH theory n (pType.mk A b) := : HH theory n (pType.mk A a) ≃g HH theory n (pType.mk A b) :=
calc HH theory n (pType.mk A a) ≃g HH theory (int.succ n) (psusp A) : by exact (Hsusp theory n (pType.mk A a)) ⁻¹ᵍ calc HH theory n (pType.mk A a) ≃g HH theory (int.succ n) (psusp A) : by exact (Hsusp theory n (pType.mk A a)) ⁻¹ᵍ
... ≃g HH theory n (pType.mk A b) : by exact Hsusp theory n (pType.mk A b) ... ≃g HH theory n (pType.mk A b) : by exact Hsusp theory n (pType.mk A b)
definition Hh_homotopy' (n : ℤ) {A B : Type*} (f : A → B) (p q : f pt = pt) theorem Hh_homotopy' (n : ℤ) {A B : Type*} (f : A → B) (p q : f pt = pt)
: Hh theory n (pmap.mk f p) ~ Hh theory n (pmap.mk f q) := λ x, : Hh theory n (pmap.mk f p) ~ Hh theory n (pmap.mk f q) := λ x,
calc Hh theory n (pmap.mk f p) x calc Hh theory n (pmap.mk f p) x
= Hh theory n (pmap.mk f p) (Hsusp theory n A ((Hsusp theory n A)⁻¹ᵍ x)) = Hh theory n (pmap.mk f p) (Hsusp theory n A ((Hsusp theory n A)⁻¹ᵍ x))
@ -41,7 +41,7 @@ namespace homology
... = Hh theory n (pmap.mk f q) x ... = Hh theory n (pmap.mk f q) x
: by exact ap (Hh theory n (pmap.mk f q)) (equiv.to_right_inv (equiv_of_isomorphism (Hsusp theory n A)) x) : by exact ap (Hh theory n (pmap.mk f q)) (equiv.to_right_inv (equiv_of_isomorphism (Hsusp theory n A)) x)
definition Hh_homotopy (n : ℤ) {A B : Type*} (f g : A →* B) (h : f ~ g) : Hh theory n f ~ Hh theory n g := λ x, theorem Hh_homotopy (n : ℤ) {A B : Type*} (f g : A →* B) (h : f ~ g) : Hh theory n f ~ Hh theory n g := λ x,
calc Hh theory n f x calc Hh theory n f x
= Hh theory n (pmap.mk f (respect_pt f)) x : by exact ap (λ f, Hh theory n f x) (pmap.eta f)⁻¹ = Hh theory n (pmap.mk f (respect_pt f)) x : by exact ap (λ f, Hh theory n f x) (pmap.eta f)⁻¹
... = Hh theory n (pmap.mk f (h pt ⬝ respect_pt g)) x : by exact Hh_homotopy' n f (respect_pt f) (h pt ⬝ respect_pt g) x ... = Hh theory n (pmap.mk f (h pt ⬝ respect_pt g)) x : by exact Hh_homotopy' n f (respect_pt f) (h pt ⬝ respect_pt g) x