Theorems · Theorem · logic and foundations
Set.mem_of_mem_of_subset
∀ {α : Type u} {x : α} {s t : Set α}, x ∈ s → s ⊆ t → x ∈ t- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 36 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 by36
Results whose statement or proof uses this declaration.
- connectedComponent_eqproof · cited by 6
- Matroid.mem_closure_iff_exists_isCircuitproof · cited by 4
- Matroid.indep_iff_forall_notMem_closure_sdiffproof · cited by 3
- Affine.Simplex.setInterior_mapproof · cited by 3
- MeasureTheory.integral_deriv_smul_comp_Ioiproof · cited by 2
- Affine.Simplex.closedInterior_face_subset_closedInteriorproof · cited by 2
- EuclideanGeometry.exists_of_range_subset_orthocentricSystemproof · cited by 2
- HahnEmbedding.Seed.mem_domain_baseEmbeddingproof · cited by 2
- EuclideanGeometry.Cospherical.affineIndependentproof · cited by 2
- Affine.Simplex.affineCombination_mem_setInterior_face_iff_memproof · cited by 2
- UniformCauchySeqOnFilter.tendstoUniformlyOnFilter_of_tendstoproof · cited by 2
- Affine.Simplex.affineSpan_range_medialproof · cited by 2