inf_iInf — Mathlib

English

The infimum of a family of pairwise minima equals the minimum of the infima: inf_i (min_j f(i,j)) = min_i inf_j f(i,j).

Русский

Инфимум семейства попарных минимумов равен минимуму инфимумов: inf_i(min_j f(i,j)) = min_i inf_j f(i,j).

LaTeX

$$$ \\inf_{i} \\min_{j} f(i,j) = \\min_{i} \\inf_{j} f(i,j). $$$

Lean4

theorem inf_iInf [Nonempty ι] {f : ι → α} {a : α} : (a ⊓ ⨅ x, f x) = ⨅ x, a ⊓ f x := by rw [iInf_inf_eq, iInf_const]

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