Theorems · Theorem · order theory

Set.iUnion_univ_pi_of_monotone

∀ {ι : Type u_1} {ι' : Type u_2} [inst : LinearOrder ι'] [Nonempty ι'] [Finite ι] {α : ι → Type u_3}
  {s : (i : ι) → ι' → Set (α i)},
  (∀ (i : ι), Monotone (s i)) → (⋃ j, Set.univ.pi fun i => s i j) = Set.univ.pi fun i => ⋃ j, s i j

Defined in: Mathlib.Data.Set.Finite.Lattice
Cited by: 1 results in Mathlib
Foundations: Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder Nonempty Finite

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Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
LinearOrderstatement and proof · cited by 8,572
Set.univstatement and proof · cited by 3,945
Finitestatement and proof · cited by 3,029
Set.iUnionstatement · cited by 2,483
Monotonestatement and proof · cited by 1,397
Set.pistatement · cited by 405
Set.finite_univproof · cited by 52
Set.iUnion_pi_of_monotoneproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

BoxIntegral.Box.iUnion_Ioo_of_tendstoproof · cited by 0