compression — Mathlib

English

If insert a s ∈ 𝓓 a 𝒜, then s ∈ 𝓓 a 𝒜.

Русский

Если insert a s ∈ 𝓓 a 𝒜, то s ∈ 𝓓 a 𝒜.

LaTeX

$$$\\text{If } (\\text{insert } a\\, s) \\in 𝓓(a,\\mathcal{A}) \\text{ then } s \\in 𝓓(a,\\mathcal{A}).$$$

Lean4

/-- To UV-compress a set family, we compress each of its elements, except that we don't want to
reduce the cardinality, so we keep all elements whose compression is already present. -/
def compression (u v : α) (s : Finset α) :=
  {a ∈ s | compress u v a ∈ s} ∪ {a ∈ s.image <| compress u v | a ∉ s}

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