Theorems · Theorem · logic and foundations
Set.mem_image
∀ {α : Type u} {β : Type v} (f : α → β) (s : Set α) (y : β), y ∈ f '' s ↔ ∃ x ∈ s, f x = y- Defined in
- Mathlib.Data.Set.Operations
- Cited by
- 131 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 12 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 by131
Results whose statement or proof uses this declaration.
- Ideal.mem_map_iff_of_surjectiveproof · cited by 19
- HahnSeries.embDomain_coeffproof · cited by 10
- Finset.sum_of_injOnproof · cited by 8
- Finsupp.span_image_eq_map_linearCombinationproof · cited by 7
- Continuous.image_connectedComponent_subsetproof · cited by 6
- Ideal.mem_map_C_iffproof · cited by 6
- MeasureTheory.Measure.haar.addIndex_elimproof · cited by 5
- MeasureTheory.Measure.haar.addIndex_posproof · cited by 5
- MeasureTheory.Measure.haar.index_elimproof · cited by 5
- MeasureTheory.Measure.haar.index_posproof · cited by 5
- Ideal.spanNorm_singletonproof · cited by 5
- Set.mem_neg_vadd_set_iffproof · cited by 5