no goals
α : Type u_1
inst✝ : Group α
s : Subgroup α
x y : α
⊢ (∃ a, ↑a * y = x) ↔ ∃ a, y * x⁻¹ = ↑a⁻¹
simp only [mul_inv_eq_iff_eq_mul, Subgroup.coe_inv, eq_inv_mul_iff_mul_eq]
no goals
α : Type u_1
inst✝ : Group α
s : Subgroup α
x y : α
⊢ (∃ a, y * x⁻¹ = ↑a⁻¹) ↔ y * x⁻¹ ∈ s
simp [exists_inv_mem_iff_exists_mem]