∀ {G : Type u_1} {M : Type u_2} {F : Type u_3} [inst : Group G] [inst_1 : Fintype G] [inst_2 : Monoid M]
  [inst_3 : DecidableEq M] [inst_4 : FunLike F G M] [MonoidHomClass F G M] (f : F) {x y : M},
  x ∈ Set.range ⇑f → y ∈ Set.range ⇑f → {g | f g = x}.card = {g | f g = y}.card