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refactor(hott/algebra/category/yoneda): reduce compilation time using 'rewrite' tactic

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Leonardo de Moura 2015-06-18 15:52:08 -07:00
parent 70fc05294b
commit 5830d7d037
1 changed files with 5 additions and 5 deletions
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hott/algebra/category/yoneda.hlean
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@ -71,10 +71,10 @@ namespace functor
theorem functor_curry_comp ⦃c c' c'' : C⦄ (f' : c' ⟶ c'') (f : c ⟶ c')
: Fhom F (f' ∘ f) = Fhom F f' ∘n Fhom F f :=
nat_trans_eq (λd, calc
natural_map (Fhom F (f' ∘ f)) d = F (f' ∘ f, id) : functor_curry_hom_def
natural_map (Fhom F (f' ∘ f)) d = F (f' ∘ f, id) : by rewrite functor_curry_hom_def
... = F (f' ∘ f, id ∘ id) : by rewrite id_comp
... = F ((f',id) ∘ (f, id)) : by esimp
... = F (f',id) ∘ F (f, id) : respect_comp F
... = F (f',id) ∘ F (f, id) : by rewrite [respect_comp F]
... = natural_map ((Fhom F f') ∘ (Fhom F f)) d : by esimp)
definition functor_curry [reducible] : C ⇒ E ^c D :=
@ -113,7 +113,7 @@ namespace functor
∘ (natural_map (to_fun_hom G f'.1) p.2 ∘ natural_map (to_fun_hom G f.1) p.2) : by esimp
... = (to_fun_hom (to_fun_ob G p''.1) f'.2 ∘ natural_map (to_fun_hom G f'.1) p'.2)
∘ (to_fun_hom (to_fun_ob G p'.1) f.2 ∘ natural_map (to_fun_hom G f.1) p.2) :
square_prepostcompose (!naturality⁻¹ᵖ) _ _
by rewrite [square_prepostcompose (!naturality⁻¹ᵖ) _ _]
... = Ghom G f' ∘ Ghom G f : by esimp
definition functor_uncurry [reducible] : C ×c D ⇒ E :=
@ -132,7 +132,7 @@ namespace functor
show (functor_uncurry (functor_curry F)) (f, g) = F (f,g),
from calc
(functor_uncurry (functor_curry F)) (f, g) = to_fun_hom F (id, g) ∘ to_fun_hom F (f, id) : by esimp
... = F (id ∘ f, g ∘ id) : respect_comp F (id,g) (f,id)
... = F (id ∘ f, g ∘ id) : by krewrite [respect_comp F (id,g) (f,id)]
... = F (f, g ∘ id) : by rewrite id_left
... = F (f,g) : by rewrite id_right,
end
@ -150,7 +150,7 @@ namespace functor
= to_fun_hom (G c) g ∘ natural_map (to_fun_hom G (ID c)) d : by esimp
... = to_fun_hom (G c) g ∘ natural_map (ID (G c)) d : by rewrite respect_id
... = to_fun_hom (G c) g ∘ id : by reflexivity
... = to_fun_hom (G c) g : id_right}
... = to_fun_hom (G c) g : by rewrite id_right}
end
theorem functor_curry_functor_uncurry : functor_curry (functor_uncurry G) = G :=