bddAbove_image2_of_bddAbove — Mathlib

English

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

Русский

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

LaTeX

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

Lean4

theorem bddAbove_image2_of_bddAbove : BddBelow s → BddAbove t → BddAbove (Set.image2 f s t) :=
  by
  rintro ⟨a, ha⟩ ⟨b, hb⟩
  exact ⟨f a b, mem_upperBounds_image2_of_mem_upperBounds_of_mem_upperBounds h₀ h₁ ha hb⟩

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