image2 — Mathlib

English

If a is greatest in s and b is least in t, then the pair (a,b) is greatest in image2 f s t.

Русский

Если a наибольший в s, а b наименьший в t, то пара (a,b) наибольшая в образе image2 f s t.

LaTeX

$$IsGreatest s a \rightarrow IsLeast t b \rightarrow IsGreatest( image2 f s t ) ( f a b )$$

Lean4

/-- See also `Monotone.map_bddAbove`. -/
protected theorem image2 : BddAbove s → BddAbove t → BddAbove (image2 f s t) :=
  by
  rintro ⟨a, ha⟩ ⟨b, hb⟩
  exact ⟨f a b, mem_upperBounds_image2 h₀ h₁ ha hb⟩

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