∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] (g : Equiv.Perm α)
  {a b : Equiv.Perm ↥g.cycleFactorsFinset},
  a ∈ {τ | ∀ (c : ↥g.cycleFactorsFinset), (↑(τ c)).support.card = (↑c).support.card} →
    b ∈ {τ | ∀ (c : ↥g.cycleFactorsFinset), (↑(τ c)).support.card = (↑c).support.card} →
      a * b ∈ {τ | ∀ (c : ↥g.cycleFactorsFinset), (↑(τ c)).support.card = (↑c).support.card}