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