Theorems · Theorem · logic and foundations
Set.subset_inter
∀ {α : Type u} {s t r : Set α}, r ⊆ s → r ⊆ t → r ⊆ s ∩ t- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 74 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
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
Cited by75
Results whose statement or proof uses this declaration.
- Filter.principalproof · cited by 740
- IsPreconnected.imageproof · cited by 24
- Set.subset_sdiff_singletonproof · cited by 14
- Matroid.Indep.subset_isBasis'_of_subsetproof · cited by 11
- IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosedproof · cited by 11
- Matroid.isBasis'_iff_isBasis_inter_groundproof · cited by 11
- Set.image_inter_subsetproof · cited by 7
- MeasureTheory.Measure.restrict_eq_selfproof · cited by 6
- Set.OrdConnected.upperClosure_inter_lowerClosureproof · cited by 5
- MeasureTheory.addHaar_image_le_mul_of_det_ltproof · cited by 4