fix(init.path): rename transport_compose to tr_compose

This commit is contained in:
Floris van Doorn 2015-08-06 15:09:49 +02:00 committed by Leonardo de Moura
parent d111607890
commit 189293b5d4
5 changed files with 8 additions and 9 deletions

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@ -154,7 +154,7 @@ namespace functor
by (cases F; apply functor_mk_eq'_idp) by (cases F; apply functor_mk_eq'_idp)
definition functor_eq_eta' {F₁ F₂ : C ⇒ D} (p : F₁ = F₂) definition functor_eq_eta' {F₁ F₂ : C ⇒ D} (p : F₁ = F₂)
: functor_eq' (ap to_fun_ob p) (!transport_compose⁻¹ ⬝ apd to_fun_hom p) = p := : functor_eq' (ap to_fun_ob p) (!tr_compose⁻¹ ⬝ apd to_fun_hom p) = p :=
begin begin
cases p, cases F₁, cases p, cases F₁,
apply concat, rotate_left 1, apply functor_eq'_idp, apply concat, rotate_left 1, apply functor_eq'_idp,

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@ -177,7 +177,7 @@ namespace is_equiv
is_equiv_rect f P df (f x) is_equiv_rect f P df (f x)
= right_inv f (f x) ▸ df (f⁻¹ (f x)) : by esimp = right_inv f (f x) ▸ df (f⁻¹ (f x)) : by esimp
... = ap f (left_inv f x) ▸ df (f⁻¹ (f x)) : by rewrite -adj ... = ap f (left_inv f x) ▸ df (f⁻¹ (f x)) : by rewrite -adj
... = left_inv f x ▸ df (f⁻¹ (f x)) : by rewrite -transport_compose ... = left_inv f x ▸ df (f⁻¹ (f x)) : by rewrite -tr_compose
... = df x : by rewrite (apd df (left_inv f x)) ... = df x : by rewrite (apd df (left_inv f x))
end end
@ -295,7 +295,7 @@ namespace equiv
equiv_rect f P df (f x) equiv_rect f P df (f x)
= right_inv f (f x) ▸ df (f⁻¹ (f x)) : by esimp = right_inv f (f x) ▸ df (f⁻¹ (f x)) : by esimp
... = ap f (left_inv f x) ▸ df (f⁻¹ (f x)) : by rewrite -adj ... = ap f (left_inv f x) ▸ df (f⁻¹ (f x)) : by rewrite -adj
... = left_inv f x ▸ df (f⁻¹ (f x)) : by rewrite -transport_compose ... = left_inv f x ▸ df (f⁻¹ (f x)) : by rewrite -tr_compose
... = df x : by rewrite (apd df (left_inv f x)) ... = df x : by rewrite (apd df (left_inv f x))

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@ -509,8 +509,7 @@ namespace eq
eq.rec_on r !idp_con⁻¹ eq.rec_on r !idp_con⁻¹
-- Transporting in a pulled back fibration. -- Transporting in a pulled back fibration.
-- rename: tr_compose definition tr_compose (P : B → Type) (f : A → B) (p : x = y) (z : P (f x)) :
definition transport_compose (P : B → Type) (f : A → B) (p : x = y) (z : P (f x)) :
transport (P ∘ f) p z = transport P (ap f p) z := transport (P ∘ f) p z = transport P (ap f p) z :=
eq.rec_on p idp eq.rec_on p idp
@ -526,7 +525,7 @@ namespace eq
apd10 (ap (λh : A → B, f ∘ h) p) a = ap f (apd10 p a) := apd10 (ap (λh : A → B, f ∘ h) p) a = ap f (apd10 p a) :=
eq.rec_on p idp eq.rec_on p idp
-- A special case of [transport_compose] which seems to come up a lot. -- A special case of [tr_compose] which seems to come up a lot.
definition tr_eq_cast_ap {P : A → Type} {x y} (p : x = y) (u : P x) : p ▸ u = cast (ap P p) u := definition tr_eq_cast_ap {P : A → Type} {x y} (p : x = y) (u : P x) : p ▸ u = cast (ap P p) u :=
eq.rec_on p idp eq.rec_on p idp

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@ -175,7 +175,7 @@ namespace pi
(λ(a : A) (b' : B' (f0⁻¹ a)), transport B (right_inv f0 a) ((f1 (f0⁻¹ a))⁻¹ b')))), (λ(a : A) (b' : B' (f0⁻¹ a)), transport B (right_inv f0 a) ((f1 (f0⁻¹ a))⁻¹ b')))),
begin begin
intro h, apply eq_of_homotopy, intro a', esimp, intro h, apply eq_of_homotopy, intro a', esimp,
rewrite [adj f0 a',-transport_compose,fn_tr_eq_tr_fn _ f1,right_inv (f1 _)], rewrite [adj f0 a',-tr_compose,fn_tr_eq_tr_fn _ f1,right_inv (f1 _)],
apply apd apply apd
end, end,
begin begin

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@ -216,7 +216,7 @@ namespace sigma
apply (sigma_eq (left_inv f a)), apply (sigma_eq (left_inv f a)),
apply pathover_of_tr_eq, apply pathover_of_tr_eq,
rewrite [▸*,adj f,-(fn_tr_eq_tr_fn (left_inv f a) (λ a, (g a)⁻¹)), rewrite [▸*,adj f,-(fn_tr_eq_tr_fn (left_inv f a) (λ a, (g a)⁻¹)),
▸*,transport_compose B' f,tr_inv_tr,left_inv] ▸*,tr_compose B' f,tr_inv_tr,left_inv]
end end
definition sigma_equiv_sigma_of_is_equiv [H1 : is_equiv f] [H2 : Π a, is_equiv (g a)] definition sigma_equiv_sigma_of_is_equiv [H1 : is_equiv f] [H2 : Π a, is_equiv (g a)]
@ -237,7 +237,7 @@ namespace sigma
-- definition ap_sigma_functor_eq (p : u.1 = v.1) (q : u.2 =[p] v.2) -- definition ap_sigma_functor_eq (p : u.1 = v.1) (q : u.2 =[p] v.2)
-- : ap (sigma_functor f g) (sigma_eq p q) = -- : ap (sigma_functor f g) (sigma_eq p q) =
-- sigma_eq (ap f p) -- sigma_eq (ap f p)
-- ((transport_compose B' f p (g u.1 u.2))⁻¹ ⬝ (fn_tr_eq_tr_fn p g u.2)⁻¹ ⬝ ap (g v.1) q) := -- ((tr_compose B' f p (g u.1 u.2))⁻¹ ⬝ (fn_tr_eq_tr_fn p g u.2)⁻¹ ⬝ ap (g v.1) q) :=
-- by induction u; induction v; apply ap_sigma_functor_eq_dpair -- by induction u; induction v; apply ap_sigma_functor_eq_dpair
/- definition 3.11.9(i): Summing up a contractible family of types does nothing. -/ /- definition 3.11.9(i): Summing up a contractible family of types does nothing. -/