Theorems · Theorem · real analysis
BoxIntegral.Box.le_iff_bounds
∀ {ι : Type u_1} {I J : BoxIntegral.Box ι}, I ≤ J ↔ J.lower ≤ I.lower ∧ I.upper ≤ J.upper- Defined in
- Mathlib.Analysis.BoxIntegral.Box.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Set.Iccproof · cited by 1,702
- BoxIntegral.Boxstatement and proof · cited by 464
- List.TFAE.outproof · cited by 177
- BoxIntegral.Box.toSetproof · cited by 121
- BoxIntegral.Box.upperstatement and proof · cited by 70
- BoxIntegral.Box.lowerstatement and proof · cited by 65
- BoxIntegral.Box.le_TFAEproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- BoxIntegral.Box.antitone_lowerproof · cited by 3
- BoxIntegral.Box.monotone_upperproof · cited by 2
- BoxIntegral.Box.face_monoproof · cited by 1
- BoxIntegral.Box.exists_seq_mono_tendstoproof · cited by 0