obtain ⟨h₁, _⟩ := h
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' : ℕ
H₁ : a = k₁ * I.a₁ + k₂' * I.a₂
H₂ : b = k₁ * I.b₁ + k₂' * I.b₂
⊢ k₁ ≤ k₂'
case 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
k₁ k₂' : ℕ
H₁ : a = k₁ * I.a₁ + k₂' * I.a₂
H₂ : b = k₁ * I.b₁ + k₂' * I.b₂
h₁ : b * (right I).a₁ ≤ a * (right I).b₁
right✝ : a * (right I).b₂ ≤ b * (right I).a₂
⊢ k₁ ≤ k₂'