∀ {S : Type u_1} [inst : Semiring S] [inst_1 : PartialOrder S] {X : Type u_2} {Y : Type u_3} [inst_2 : Fintype X]
  [inst_3 : Fintype Y] [inst_4 : IsOrderedRing S] (f f_1 : X → Y),
  f = f_1 → ∀ (s s_1 : ↑(stdSimplex S X)), s = s_1 → stdSimplex.map f s = stdSimplex.map f_1 s_1