instInvolutiveStar — Mathlib

English

The set of subsets Set α inherits an involutive star from α; in particular, s⋆⋆ = s for all s ⊆ α.

Русский

Множество подмножеств Set α наследует инволютивную звезду от α; в частности, (s⋆)⋆ = s для всех s ⊆ α.

LaTeX

$$$\\text{InvolutiveStar}(\\,Set\\, α\\compagnate)\\;: \\; (s^{\\star})^{\\star} = s.$$$

Lean4

@[simp]
instance [InvolutiveStar α] : InvolutiveStar (Set α)
    where
  star := Star.star
  star_involutive s := by simp only [← star_preimage, preimage_preimage, star_star, preimage_id']

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