mem_compression — Mathlib

English

A variant of the disjoint-and-le compression identity with alternate assumptions.

Русский

Вариант тождества компрессии при раздельности и не стандартных предпосылках.

LaTeX

$$$\\mathrm{UV.compress\\_of\\_disjoint\\_of\\_le'} (hva : Disjoint v a) (hua : u ≤ a) : \\mathrm{compress}~u~v~(a) = a$$$

Lean4

/-- `a` is in the UV-compressed family iff it's in the original and its compression is in the
original, or it's not in the original but it's the compression of something in the original. -/
theorem mem_compression : a ∈ 𝓒 u v s ↔ a ∈ s ∧ compress u v a ∈ s ∨ a ∉ s ∧ ∃ b ∈ s, compress u v b = a := by
  simp_rw [compression, mem_union, mem_filter, mem_image, and_comm]

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