Theorems · Theorem · order theory
Set.mem_insert_iff
∀ {α : Type u_1} {x a : α} {s : Set α}, x ∈ insert a s ↔ x = a ∨ x ∈ s- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 39 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 by39
Results whose statement or proof uses this declaration.
- collinear_pairproof · cited by 8
- iInf_insertproof · cited by 5
- Finset.iInf_insertproof · cited by 5
- Vitali.exists_disjoint_subfamily_covering_enlargementproof · cited by 3
- Set.indicator_const_preimageproof · cited by 2
- ArchimedeanClass.mk_sumproof · cited by 2
- Sbtw.dist_lt_max_distproof · cited by 2
- Function.range_subset_insert_image_supportproof · cited by 2
- MeasureTheory.LocallyIntegrableOn.exists_nat_integrableOnproof · cited by 2
- AnalyticAt.preimage_of_nhdsNEproof · cited by 2
- MulAction.isMultiplyPreprimitive_succ_iff_ofStabilizerproof · cited by 2