∀ {X : Type u_2} [inst : Fintype X] {𝕜 : Type u_5} [inst_1 : Field 𝕜] [inst_2 : LinearOrder 𝕜]
  [inst_3 : IsStrictOrderedRing 𝕜] [inst_4 : Nonempty X] [inst_5 : DecidableEq X],
  ↑stdSimplex.barycenter = Finset.univ.centerMass (fun x => 1) fun i => Pi.single i 1