continuous_min — Mathlib

English

The map (a,b) ↦ min(a,b) from α×α to α is continuous when α is ordered with OrderClosedTopology.

Русский

Отображение (a,b) ↦ min(a,b) из α×α в α непрерывно при упорядоченной структуре α с OrderClosedTopology.

LaTeX

$$$\text{Continuous}(p \mapsto \min(p_1,p_2))$ for $p = (p_1,p_2) \in \alpha \times \alpha$ given $\alpha$ with an OrderClosedTopology.$$

Lean4

theorem continuous_min : Continuous fun p : α × α => min p.1 p.2 :=
  continuous_fst.min continuous_snd

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