sup_image₂_left — Mathlib

English

Dual to the left version: sup' (image₂ f s t) h g = sup' t h.of_image₂_right (fun y => sup' s h.of_image₂_left (g (f · y))).

Русский

Дуальная левая версия: sup' (image₂ f s t) = sup' t ...

LaTeX

$$$\\forall s:\\ Finset, t:\\ Finset, sup' (image_2 f s t) h g = sup' t h.of_image_2_right (\\lambda y, sup' s h.of_image_2_left (g (f \\cdot y)))$$$

Lean4

theorem sup_image₂_left (g : γ → δ) : sup (image₂ f s t) g = sup s fun x ↦ sup t (g <| f x ·) := by
  simp only [image₂, sup_image, sup_product_left]; rfl

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