Deleting one point preserves convex independence

import Definitions.Def_Erdos9796Counting_Adapter
import Definitions.Def_Erdos9796Counting_Foundation
import Mathlib.Analysis.Convex.Between
import Mathlib.Analysis.Convex.Independent
import Mathlib.Data.Finset.Basic
import Mathlib.Geometry.Euclidean.Angle.Oriented.Basic
open Problem97 Problem97.ConvexIndep
open scoped EuclideanGeometry

theorem Batch3N9.Problem97.ConvexIndep.erase {A : Finset ℝ²} (x : ℝ²) (hA : ConvexIndep A) : ConvexIndep (A.erase x) := by sorry