Theorems · Theorem · logic and foundations
Set.mem_range
∀ {α : Type u} {ι : Sort u_1} {f : ι → α} {x : α}, x ∈ Set.range f ↔ ∃ y, f y = x- Defined in
- Mathlib.Data.Set.Operations
- Cited by
- 102 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 11 definitions · 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.
Cited by102
Results whose statement or proof uses this declaration.
- WithBot.range_coeproof · cited by 15
- Topology.IsClosedEmbedding.map_tsumproof · cited by 6
- Dynamics.coverMincard_finite_iffproof · cited by 6
- LowerSet.coe_iSupproof · cited by 5
- HasSum.of_nat_of_neg_add_oneproof · cited by 5
- LowerSet.coe_iInfproof · cited by 4
- AddMonoidHom.exists_mrange_eq_mgraphproof · cited by 4
- iInf_le_iffproof · cited by 4
- borel_eq_generateFrom_Iicproof · cited by 4
- MeasureTheory.IsStronglyPredictable.of_measurable_add_oneproof · cited by 4
- MonoidWithZeroHom.ValueGroup₀.restrict₀_surjectiveproof · cited by 3
- Function.Exact.iff_rangeFactorizationproof · cited by 3