simp only [toColex_inj, ofColex_toColex, ne_eq, and_imp]
case a.mpr
α : Type u_1
inst✝¹ : LinearOrder α
𝒜 𝒜₁ 𝒜₂ : Finset (Finset α)
s t✝ : Finset α
r : ℕ
inst✝ : Fintype α
hs : s.Nonempty
t : Finset α
⊢ (s.erase (s.min' hs)).card = t.card ∧
      ({ ofColex := t } = { ofColex := s.erase (s.min' hs) } ∨
        ∃ w ∈ s.erase (s.min' hs), w ∉ t ∧ ∀ ⦃a : α⦄, w < a → (a ∈ t ↔ a ∈ s.erase (s.min' hs))) →
    ∃ a ∉ t,
      s.card = (insert a t).card ∧
        ({ ofColex := insert a t } = { ofColex := s } ∨
          ∃ w ∈ s, w ∉ insert a t ∧ ∀ ⦃a_1 : α⦄, w < a_1 → (a_1 ∈ insert a t ↔ a_1 ∈ s))
case a.mpr
α : Type u_1
inst✝¹ : LinearOrder α
𝒜 𝒜₁ 𝒜₂ : Finset (Finset α)
s t✝ : Finset α
r : ℕ
inst✝ : Fintype α
hs : s.Nonempty
t : Finset α
⊢ (s.erase (s.min' hs)).card = t.card →
    (t = s.erase (s.min' hs) ∨
        ∃ w ∈ s.erase (s.min' hs), w ∉ t ∧ ∀ ⦃a : α⦄, w < a → (a ∈ t ↔ a ∈ s.erase (s.min' hs))) →
      ∃ a ∉ t,
        s.card = (insert a t).card ∧
          (insert a t = s ∨ ∃ w ∈ s, w ∉ insert a t ∧ ∀ ⦃a_1 : α⦄, w < a_1 → (a_1 ∈ insert a t ↔ a_1 ∈ s))