Definition indexed_carrier_to_carrier_union {X I : UU} (index : I → hsubtype X) : (∑ (i : I), (carrier (index i))) → (carrier (⋃ index)). Proof. intro h. exact(pr12 h ,, hinhpr (pr1 h ,, pr22 h)). Defined.
Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.Combinatorics.FiniteSets. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.MoreFoundations.Subtypes. Require Import UniMath.Combinatorics.KFiniteTypes.