Theorems · Theorem · logic and foundations
Set.inter_eq_right
∀ {α : Type u} {s t : Set α}, s ∩ t = t ↔ t ⊆ s- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- inf_eq_rightproof · cited by 64
Cited by41
Results whose statement or proof uses this declaration.
- Set.inter_eq_self_of_subset_rightproof · cited by 39
- Real.Gamma_pos_of_posproof · cited by 17
- IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosedproof · cited by 11
- IsPreconnected.subset_connectedComponentInproof · cited by 6
- MeasureTheory.LocallyIntegrableOn.aestronglyMeasurableproof · cited by 6
- quasispectrum.mul_commproof · cited by 3
- Metric.cthickening_eq_iInter_thickeningproof · cited by 3
- ProbabilityTheory.setBernoulli_singletonproof · cited by 3
- Set.image_subtype_val_Ici_Iciproof · cited by 2
- Set.image_subtype_val_Ici_Ioiproof · cited by 2
- tendsto_setIntegral_peak_smul_of_integrableOn_of_tendstoproof · cited by 2
- Dynamics.coverEntropy_restrict_subsetproof · cited by 2