∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] (f g : Equiv.Perm α),
  (∀ {x : α}, g x ≠ x → f.cycleOf x = g.cycleOf x) →
    ∀ (x : α),
      ¬g x = x →
        ∀ (m : List (Equiv.Perm α)),
          m.prod = (f.cycleOf x)⁻¹ * g ∧ (∀ g' ∈ m, g'.IsCycle) ∧ List.Pairwise Equiv.Perm.Disjoint m →
            (f.cycleOf x :: m).prod = g ∧
              (∀ g' ∈ f.cycleOf x :: m, g'.IsCycle) ∧ List.Pairwise Equiv.Perm.Disjoint (f.cycleOf x :: m)