Theorems · Theorem · order theory
Set.biInter_subset_of_mem
∀ {α : Type u_1} {β : Type u_2} {s : Set α} {t : α → Set β} {x : α}, x ∈ s → ⋂ x ∈ s, t x ⊆ t xA specialization of iInter₂_subset.
- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 61 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
- Set.iInter₂_subsetproof · cited by 15
Cited by18
Results whose statement or proof uses this declaration.
- Set.biInter_subset_biInter_leftproof · cited by 9
- ProbabilityTheory.Kernel.IndepSets.bInterproof · cited by 2
- Matroid.Indep.inter_isBasis_biInterproof · cited by 2
- Set.dissipate_subsetproof · cited by 2
- AffineSubspace.direction_sInfproof · cited by 2
- MulAction.IsPreprimitive.exists_mem_smul_and_notMem_smulproof · cited by 1
- MeasureTheory.aemeasurable_of_exist_almost_disjoint_supersetsproof · cited by 1
- MulAction.IsBlock.of_subsetproof · cited by 1
- mem_generatePiSystem_iUnion_elimproof · cited by 1
- SequentiallyComplete.setSeq_sub_auxproof · cited by 1
- AddAction.IsBlock.of_subsetproof · cited by 1
- Filter.HasBasis.pi_selfproof · cited by 1