Theorems · Theorem · real analysis
BoxIntegral.Prepartition.compl_congr
∀ {ι : Type u_1} {I : BoxIntegral.Box ι} [inst : Finite ι] {π₁ π₂ : BoxIntegral.Prepartition I},
π₁.iUnion = π₂.iUnion → π₁.compl = π₂.complSince the definition of BoxIntegral.Prepartition.compl uses Exists.choose,
the result depends only on π.iUnion.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
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 and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Finitestatement and proof · cited by 3,029
- BoxIntegral.Boxstatement and proof · cited by 464
- BoxIntegral.Prepartitionstatement and proof · cited by 199
- BoxIntegral.Box.toSetproof · cited by 121
- BoxIntegral.Prepartition.iUnionstatement and proof · cited by 71
- BoxIntegral.Prepartition.complstatement · cited by 12
- BoxIntegral.Prepartition.exists_iUnion_eq_sdiffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- BoxIntegral.IntegrationParams.exists_memBaseSet_le_iUnion_eqproof · cited by 2