simpa using open_leastNumber (P := fun u ↦ b * u ≤ a) ⟨“x | &b * x ≤ &a”, by simp, by intro x; simp⟩
M : Type u_1
inst✝⁶ : Zero M
inst✝⁵ : One M
inst✝⁴ : Add M
inst✝³ : Mul M
inst✝² : LT M
inst✝¹ : M ⊧ₘ* 𝐏𝐀⁻
inst✝ : M ⊧ₘ* 𝐈open
a b : M
pos : 0 < b
⊢ a < b * (a + 1) → ∃ u, b * u ≤ a ∧ a < b * (u + 1)
no goals