fact: Definition Book_2_7 {A B : Type} {P : A -> Type} {Q : B -> Type} (f : A -> B) (g : forall a, P a -> Q (f a)) (u v : sig P) (p : u.1 = v.1) (q : p # u.2 = v.2) : ap (functor_sigma f g) (path_sigma P u v p q) = path_sigma Q (functor_sigma f g u) (functor_sigma f g v) (ap f p) ((transport_compose Q f p (g u.1 u.2))^ @ (@ap_transport _ P (fun x => Q (f x)) _ _ p g u.2)^ @ ap (g v.1) q).
imports: HoTT(Basics Types HProp HSet Projective TruncType Truncations Modalities.Notnot Modalities.Open Modalities.Closed BoundedSearch Equiv.BiInv Spaces.Nat Spaces.Torus.TorusEquivCircles Metatheory.Core Metatheory.FunextVarieties)