case h
α : Type u_1
s : Cycle α
h✝ : Subsingleton s
l : List α
h : Subsingleton (Quot.mk Setoid.r l)
⊢ ∀ ⦃x : α⦄, x ∈ Quot.mk Setoid.r l → ∀ ⦃y : α⦄, y ∈ Quot.mk Setoid.r l → x = y
α : Type u_1
s : Cycle α
h : Subsingleton s
⊢ ∀ ⦃x : α⦄, x ∈ s → ∀ ⦃y : α⦄, y ∈ s → x = y
induction' s using Quot.inductionOn with l
case h
α : Type u_1
s : Cycle α
h✝ : Subsingleton s
l : List α
h : l = [] ∨ ∃ a, l = [a]
⊢ ∀ ⦃x : α⦄, x ∈ Quot.mk Setoid.r l → ∀ ⦃y : α⦄, y ∈ Quot.mk Setoid.r l → x = y
case h
α : Type u_1
s : Cycle α
h✝ : Subsingleton s
l : List α
h : Subsingleton (Quot.mk Setoid.r l)
⊢ ∀ ⦃x : α⦄, x ∈ Quot.mk Setoid.r l → ∀ ⦃y : α⦄, y ∈ Quot.mk Setoid.r l → x = y
simp only [length_subsingleton_iff, length_coe, mk_eq_coe, le_iff_lt_or_eq, Nat.lt_add_one_iff,
  length_eq_zero, length_eq_one, Nat.not_lt_zero, false_or_iff] at h
no goals
case h
α : Type u_1
s : Cycle α
h✝ : Subsingleton s
l : List α
h : l = [] ∨ ∃ a, l = [a]
⊢ ∀ ⦃x : α⦄, x ∈ Quot.mk Setoid.r l → ∀ ⦃y : α⦄, y ∈ Quot.mk Setoid.r l → x = y
rcases h with (rfl | ⟨z, rfl⟩) <;> simp