proposition: Lemma iskfinite_union {I X : UU} (index : I → hsubtype X) (Ifinite : isfinite I) (index_finite : ∏ (i : I), iskfinite (index i)) : iskfinite (⋃ index).
proof: Proof. assert(finitechoicebase : ∥ ∏ (i : I), kfinstruct (index i) ∥). { use ischoicebasefiniteset. apply Ifinite. apply index_finite. } use(hinhfun2 _ Ifinite finitechoicebase). intro; apply kfinstruct_union. now apply kfinstruct_finstruct. Qed.
imports: UniMath.Foundations.Propositions UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Notations UniMath.Combinatorics.FiniteSets UniMath.Combinatorics.StandardFiniteSets UniMath.MoreFoundations.Subtypes UniMath.Combinatorics.KFiniteTypes