Theorems · Theorem · real analysis
BoxIntegral.Box.mem_univ_Ioc
∀ {ι : Type u_1} {x : ι → ℝ} {I : BoxIntegral.Box ι}, (x ∈ Set.univ.pi fun i => Set.Ioc (I.lower i) (I.upper i)) ↔ x ∈ I- Defined in
- Mathlib.Analysis.BoxIntegral.Box.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.univstatement · cited by 3,945
- Set.Iocstatement · cited by 971
- BoxIntegral.Boxstatement and proof · cited by 464
- Set.pistatement · cited by 405
- BoxIntegral.Box.upperstatement · cited by 70
- BoxIntegral.Box.lowerstatement · cited by 65
- Set.mem_univ_piproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- BoxIntegral.Box.coe_eq_piproof · cited by 9