Theorems · Theorem · real analysis
BoxIntegral.Box.le_TFAE
∀ {ι : Type u_1} (I J : BoxIntegral.Box ι),
[I ≤ J, ↑I ⊆ ↑J, Set.Icc I.lower I.upper ⊆ Set.Icc J.lower J.upper, J.lower ≤ I.lower ∧ I.upper ≤ J.upper].TFAE- Defined in
- Mathlib.Analysis.BoxIntegral.Box.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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.univproof · cited by 3,945
- Set.Iccstatement and proof · cited by 1,702
- closureproof · cited by 1,254
- Set.Iocproof · cited by 971
- BoxIntegral.Boxstatement and proof · cited by 464
- Set.piproof · cited by 405
- closure_monoproof · cited by 133
- BoxIntegral.Box.toSetstatement and proof · cited by 121
- List.TFAEstatement · cited by 102
- List.tfae_of_cycleproof · cited by 83
Cited by2
Results whose statement or proof uses this declaration.
- BoxIntegral.Box.le_iff_boundsproof · cited by 4
- BoxIntegral.Box.le_iff_Iccproof · cited by 3