Theorems · Theorem · logic and foundations
Set.mem_of_subset_of_mem
∀ {α : Type u} {s₁ s₂ : Set α} {a : α}, s₁ ⊆ s₂ → a ∈ s₁ → a ∈ s₂- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 48 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 by48
Results whose statement or proof uses this declaration.
- Set.notMem_subsetproof · cited by 18
- UniqueDiffWithinAt.monoproof · cited by 8
- Finsupp.mapDomain_of_notMem_rangeproof · cited by 7
- gauge_monoproof · cited by 4
- ProbabilityTheory.Kernel.indepSets_of_indepSets_of_le_leftproof · cited by 3
- aeSeq.prop_of_mem_aeSeqSetproof · cited by 3
- Convex.helly_theorem'proof · cited by 3
- HahnEmbedding.Partial.mem_domainproof · cited by 2
- rieszContentAux_unionproof · cited by 2
- ProbabilityTheory.Kernel.indepSets_of_indepSets_of_le_rightproof · cited by 2
- JacobsonNoether.exists_pow_mem_center_of_inseparableproof · cited by 2
- UniformSpace.hausdorff.isClosed_setOfPred_totallyBoundedproof · cited by 2