Theorems · Theorem · logic and foundations
Set.inter_subset_inter_left
∀ {α : Type u} {s t : Set α} (u : Set α), s ⊆ t → s ∩ u ⊆ t ∩ u- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, 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.Subset.rflproof · cited by 255
- Set.inter_subset_interproof · cited by 66
Cited by36
Results whose statement or proof uses this declaration.
- Matroid.closure_subset_closureproof · cited by 24
- MDifferentiableWithinAt.monoproof · cited by 10
- MeasureTheory.measure_le_setAverage_posproof · cited by 5
- Set.InjOn.image_subset_image_iffproof · cited by 4
- Metric.finite_isBounded_inter_isClosedproof · cited by 4
- frontier_inter_subsetproof · cited by 4
- isPreconnected_univ_piproof · cited by 4
- MeasureTheory.Measure.exists_isOpen_everywherePosSubset_eq_sdiffproof · cited by 4
- SmoothBumpFunction.tsupport_subset_symm_image_closedBallproof · cited by 3
- IsStationary.monoproof · cited by 2
- MeasureTheory.OuterMeasure.ofFunction_caratheodoryproof · cited by 2
- VectorField.mpullbackWithin_mlieBracketWithin'proof · cited by 2