Theorems · Theorem · logic and foundations
Set.nonempty_of_mem
∀ {α : Type u} {s : Set α} {x : α}, x ∈ s → s.Nonempty- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
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
- Set.Nonemptystatement · cited by 2,627
Cited by19
Results whose statement or proof uses this declaration.
- le_csSupproof · cited by 66
- csInf_leproof · cited by 51
- CompleteLattice.isCompactElement_iff_exists_le_sSup_of_le_sSupproof · cited by 4
- AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonposproof · cited by 4
- HahnSeries.orderTop_eq_of_leproof · cited by 3
- MeasureTheory.stoppedValue_hittingBtwn_memproof · cited by 3
- DirichletCharacter.conductor_mem_conductorSetproof · cited by 3
- Int.absNorm_under_eq_sInfproof · cited by 2
- MulAction.IsPreprimitive.is_two_motive_of_is_motiveproof · cited by 2
- Dynamics.coverMincard_le_netMaxcardproof · cited by 2
- DiffContOnCl.two_pi_i_inv_smul_circleIntegral_sub_inv_smulproof · cited by 1
- MeasureTheory.norm_resolvent_le_inv_infDist_supportproof · cited by 1