Theorems · Theorem · order theory
Function.Injective.mem_set_image
∀ {α : Type u_1} {β : Type u_2} {f : α → β}, Function.Injective f → ∀ {s : Set α} {a : α}, f a ∈ f '' s ↔ a ∈ s- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
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 by53
Results whose statement or proof uses this declaration.
- Set.smul_mem_smul_set_iffproof · cited by 14
- Set.vadd_mem_vadd_set_iffproof · cited by 10
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- linearIndependent_iff_card_eq_finrank_spanproof · cited by 5
- sbtw_lineMap_iffproof · cited by 4
- LinearOrderedField.coe_mem_cutMap_iffproof · cited by 4
- ConvexIndependent.comp_embeddingproof · cited by 4
- dist_add_dist_eq_iffproof · cited by 4
- IntermediateField.mem_liftproof · cited by 4
- Function.Injective.wbtw_map_iffproof · cited by 3
- Equiv.Set.image_symm_applystatement · cited by 3
- affineIndependent_set_iff_linearIndependent_vsubproof · cited by 3