proposition: Lemma issurjective_indexed_carrier_to_union {X I : UU} (index : I → hsubtype X) : issurjective (indexed_carrier_to_carrier_union index).
proof: Proof. intros [x in_union]. use(hinhfun _ in_union). intros [i in_index]. use make_hfiber. - exact(i ,, x ,, in_index). - now apply subtypePath_prop. Qed.
imports: UniMath.Foundations.Propositions UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Notations UniMath.Combinatorics.FiniteSets UniMath.Combinatorics.StandardFiniteSets UniMath.MoreFoundations.Subtypes UniMath.Combinatorics.KFiniteTypes