proposition: Lemma transportf_isotoid_dep' (J : UU) (C : precategory) (F : J -> C) (a a' : C) (p : a = a') (f : ∏ c, a --> F c) : transportf (λ x : C, ∏ c, x --> F c) p f = λ c, idtoiso (!p) · f c.
proof: Proof. now destruct p; apply funextsec; intro x; rewrite id_left. Defined.
imports: UniMath.Foundations.PartA UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos