compress_of_disjoint_of_le' — Mathlib

English

A variant of the disjoint-and-le compression formula with alternative ordering of arguments.

Русский

Вариант формулы компрессии при раздельности и альтернативном порядке аргументов.

LaTeX

$$$\\text{compress of disjoint of le'}: \\mathrm{compress} \\ v\\ a \\ b = \\mathrm{something}$$$

Lean4

theorem compress_of_disjoint_of_le' (hva : Disjoint v a) (hua : u ≤ a) : compress u v ((a ⊔ v) \ u) = a := by
  rw [compress_of_disjoint_of_le disjoint_sdiff_self_right
      (le_sdiff.2 ⟨(le_sup_right : v ≤ a ⊔ v), hva.mono_right hua⟩),
    sdiff_sup_cancel (le_sup_of_le_left hua), hva.symm.sup_sdiff_cancel_right]

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