mk_iUnion_Ordinal_le_of_le — Mathlib

English

Let ho express o.card ≤ c and hc express ℵ0 ≤ c; for A: Ordinal → Set β with ∀ j < o, #(A j) ≤ c, then #(⋃ j < o, A j) ≤ c.

Русский

Пусть ho задаёт o.card ≤ c и hc задаёт ℵ0 ≤ c; для A: Ordinal → Set β с ∀ j < o, #(A j) ≤ c, тогда #(⋃ j < o, A j) ≤ c.

LaTeX

$$$\#\bigcup_{j

Lean4

theorem mk_iUnion_Ordinal_le_of_le {β : Type*} {o : Ordinal} {c : Cardinal} (ho : o.card ≤ c) (hc : ℵ₀ ≤ c)
    (A : Ordinal → Set β) (hA : ∀ j < o, #(A j) ≤ c) : #(⋃ j < o, A j) ≤ c :=
  by
  apply mk_iUnion_Ordinal_lift_le_of_le _ hc A hA
  rwa [Cardinal.lift_le]

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