image_image₂ — Mathlib

English

The image of the pair constructor is the cartesian product constructed by the product operator: image₂ Prod.mk s t = s ×ˢ t.

Русский

Образ пары отобразителя равен декартову произведению, заданному через ⋅: image₂ Prod.mk s t = s ×ˢ t.

LaTeX

$$$\mathrm{image}_2\mathrm{ Prod.mk}\ s\ t = s \times\!\!\ˢ t$$$

Lean4

theorem image_image₂ (f : α → β → γ) (g : γ → δ) : (image₂ f s t).image g = image₂ (fun a b => g (f a b)) s t :=
  coe_injective <| by
    push_cast
    exact image_image2 _ _

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