Theorems · Theorem · order theory
Set.iInter_exists
∀ {α : Type u_1} {ι : Sort u_5} {p : ι → Prop} {f : Exists p → Set α}, ⋂ (x : Exists p), f x = ⋂ i, ⋂ (h : p i), f ⋯- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 44 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_existsproof · cited by 6
Cited by44
Results whose statement or proof uses this declaration.
- Set.iInter_iInter_eq'proof · cited by 22
- Submodule.coe_iInfproof · cited by 16
- Subfield.coe_sInfproof · cited by 5
- LowerSet.coe_iInfproof · cited by 4
- UpperSet.coe_iSupproof · cited by 4
- ProbabilityTheory.Kernel.iIndepSets.precompproof · cited by 4
- Matroid.closure_iInter_eq_iInter_closure_of_iUnion_indepproof · cited by 3
- NonUnitalAlgebra.coe_iInfproof · cited by 3
- Algebra.coe_iInfproof · cited by 3
- NonUnitalStarAlgebra.coe_iInfproof · cited by 2
- LieSubalgebra.coe_sInfproof · cited by 2
- Algebra.sInf_toSubsemiringproof · cited by 2