case h
R : Type u_2
M : Type u_1
inst✝² : CommSemiring R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
s : Set R
a : R
x : M
⊢ x ∈ torsionBySet R M {a} ↔ x ∈ torsionBy R M a
R : Type u_2
M : Type u_1
inst✝² : CommSemiring R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
s : Set R
a : R
⊢ torsionBySet R M {a} = torsionBy R M a
ext x
no goals
case h
R : Type u_2
M : Type u_1
inst✝² : CommSemiring R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
s : Set R
a : R
x : M
⊢ x ∈ torsionBySet R M {a} ↔ x ∈ torsionBy R M a
simp only [mem_torsionBySet_iff, SetCoe.forall, Subtype.coe_mk, Set.mem_singleton_iff,
  forall_eq, mem_torsionBy_iff]