bddBelow_image2_of_bddAbove — Mathlib

English

If s is bounded above and t is bounded above, then image2 f s t is bounded below.

Русский

Если s ограничено сверху и t ограничено сверху, то image2 f s t ограничено снизу.

LaTeX

$$BddAbove s → BddAbove t → BddBelow (Set.image2 f s t)$$

Lean4

theorem bddBelow_image2_of_bddAbove : BddAbove s → BddBelow t → BddBelow (Set.image2 f s t) :=
  by
  rintro ⟨a, ha⟩ ⟨b, hb⟩
  exact ⟨f a b, mem_lowerBounds_image2_of_mem_lowerBounds_of_mem_lowerBounds h₀ h₁ ha hb⟩

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