Theorems · Theorem · real analysis
BoxIntegral.Prepartition.eq_of_mem_of_mem
∀ {ι : Type u_1} {I J₁ J₂ : BoxIntegral.Box ι} (π : BoxIntegral.Prepartition I) {x : ι → ℝ},
J₁ ∈ π → J₂ ∈ π → x ∈ J₁ → x ∈ J₂ → J₁ = J₂- Cited by
- 6 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- BoxIntegral.Boxstatement and proof · cited by 464
- BoxIntegral.Prepartitionstatement and proof · cited by 199
- by_contraproof · cited by 60
- Disjoint.le_botproof · cited by 52
- BoxIntegral.Prepartition.disjoint_coe_of_memproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- BoxIntegral.Prepartition.eq_of_le_of_leproof · cited by 3
- BoxIntegral.Prepartition.eq_of_boxes_subset_iUnion_supersetproof · cited by 2
- BoxIntegral.Prepartition.restrict_biUnionproof · cited by 2
- BoxIntegral.Prepartition.injOn_setOfPred_mem_Icc_setOfPred_lower_eqproof · cited by 2
- BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_iUnion_subsetproof · cited by 2
- BoxIntegral.Prepartition.IsPartition.existsUniqueproof · cited by 0