Theorems · Theorem · order theory
Set.iInter_iInter_eq_left
∀ {α : Type u_1} {β : Type u_2} {b : β} {s : (x : β) → x = b → Set α}, ⋂ x, ⋂ (h : x = b), s x h = s b ⋯- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Set.iInterstatement · cited by 1,084
- iInf_iInf_eq_leftproof · cited by 12
Cited by18
Results whose statement or proof uses this declaration.
- Set.iInter_iInter_eq_or_leftproof · cited by 8
- Set.dissipate_zero_natproof · cited by 2
- TopCat.isTopologicalBasis_cofiltered_limitproof · cited by 1
- generateFrom_piiUnionInter_singleton_leftproof · cited by 1
- MeasureTheory.mem_generateSetAlgebra_elimproof · cited by 1
- Dynamics.dynEntourage_oneproof · cited by 1
- Set.exists_subset_dissipate_of_directedproof · cited by 1
- mem_generatePiSystem_iUnion_elimproof · cited by 1
- Filter.biInter_mem'proof · cited by 1
- piiUnionInter_singletonproof · cited by 1
- IsPiSystem.biInter_memproof · cited by 1
- AlgebraicGeometry.RingedSpace.zeroLocus_singletonproof · cited by 1