refine ⟨k₁, k₂, ?_, ?_⟩ <;> linarith
case right.intro.intro.intro
a b : ℕ
I : BasicInterval
ih : mem a b I → ∃ k₁ k₂, a = k₁ * I.a₁ + k₂ * I.a₂ ∧ b = k₁ * I.b₁ + k₂ * I.b₂
h : mem a b (right I)
k₁ k₂' k₂ : ℕ
H₂ : b = k₁ * I.b₁ + (k₂ + k₁) * I.b₂
H₁ : a = k₁ * I.a₁ + (k₂ + k₁) * I.a₂
hk : k₂' = k₂ + k₁
⊢ ∃ k₁ k₂, a = k₁ * (I.a₁ + I.a₂) + k₂ * I.a₂ ∧ b = k₁ * (I.b₁ + I.b₂) + k₂ * I.b₂
no goals